This section is mainly concerned with an attempt to develop an intuitive understanding of the exergy equations developed in the previous section, by considering reversible equivalent circuits of some common adiabatic components. We repeat equations (3), (4) and (5) developed in Chapter 7a on the exergy analysis of a control volume.
Note that the reversible work wrev will either be the maximum available output work for work producing devices, or the minimum possible input work (negative value) for work absorbing devices.
We now consider the Energy and Entropy Generation equations for adiabatic components (q = 0):
Applying all the above analysis to evaluating the Second Law Efficiencies (ηII) of adiabatic work absorbing and work producing components we obtain:
We now apply the above Second Law analysis to an adiabatic refrigeration compressor. We wish to determine the minimum work wC rev required to drive the compressor between the inlet state (1) and the exit state (2). Note that the isentropic compression that we evaluated in Chapter 6 will not provide the answer, since state (2s) is not the same as the actual state (2).
The above equations are in fact correct however we have difficulty in understanding their significance. In examining the adiabatic compressor above we cannot understand why the environment (dead space) temperature T0 features so prominently in the equations, when in fact there seems to be no obvious interaction between the adiabatic compressor and the environment. Note that as far as the adiabatic compressor is concerned we will assume that the surroundings temperature T0 is equal to the exit temperature.
In an attempt to find some intuitive meaning to these equations we consider a reversible system having the same inlet and exit states as our actual compressor. This comprises a three component system consisting of an inlet heat exchanger, a reversible heat engine and an isentropic compressor as shown below:
A typical h-s diagram for this system is shown below, in which we have used typical inlet conditions of 140kPa, -10°C and exit conditions of 700kPa, 60°C. The reversible heat engine will provide extra work to drive the compressor, absorbing its heat from the environment temperature T0 while rejecting heat to the heat exchanger. The exit state (2) from the heat exchanger has been chosen such that the compression process (2) - (3) will be isentropic.
We now derive the exergy equations for the three component system above, and consider first the heat engine. Since the temperature T of the heat exchanger varies from the inlet temperature T1 to the outlet temperature T2, we use the differential energy equation form for the reversible heat engine.
Since T0 is constant, this equation can be integrated from the inlet state (1) to the outlet state (2), leading to:
This familiar final form was to be expected. The net minimum work required to drive the compressor is thus:determined as follows:
Notice that this result is identical to that shown above for the actual adiabatic compressor, since we added the heat exchanger, thus state (3) is in fact equivalent to the original state (2).
Problem 7.4 - Recall Solved Problem 6.5 in which we evaluated the Adiabatic Efficiency (ηC) of a refrigeration compressor, and determined it to be 92%. Redo this problem and determine the Second Law Efficiency (ηII) of this compressor. [92%]
We now apply the above Second Law Analysis to an adiabatic steam turbine. We wish to determine the maximum available turbine work output wT rev between the inlet state (1) and the exit state (2). We will then be able to determine the second law eficiency by comparing the actual work output to the reversible (maximum available) work output as follows:
Once again, in an attempt to find some intuitive meaning to these equations we consider a reversible system having the same inlet and exit states as the actual turbine, comprising an isentropic turbine, a heat pump pumping heat from the surroundings to the heat exchanger in the exit stream. Note that as far as the adiabatic turbine is concerned we will assume that the surroundings temperature T0 is equal to the exit temperature.
The h-s diagram for this system is shown below, in which we have chosen as an example a steam turbine having inlet conditions 6MPa, 600°C, and outlet conditions 50kPa, 100°C.
Notice from the h-s diagram that the heat exchanger temperature varies from the saturation temperature at 50 kPa (81°C) to 100°C at state (3). In order to accommodate that change we develop the differential form of the heat pump as follows:
Since T0 is constant, this differential equation can be integrated from state (2) to state (3).
We can then subtract the work provided to the heat pump from the output work of the turbine leading to the final form of the maximum available work, as follows:
Notice that this result is identical to that shown in the box above for the actual adiabatic turbine, since state (3) is in fact equivalent to the original state (2).
Problem 7.5 - Recall Solved Problem 6.1 in which we evaluated the Adiabatic Efficiencies (ηT) of both the High Pressure and the Low Pressure steam turbines of the supercritical steam power plantand found them to be 77% and 90% respectively. Redo this problem and determine the respective Second Law Efficiencies (ηII) of both turbines. [77%, 90%]
Engineering Thermodynamics by Israel Urieli is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 United States License


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ZIM-X provides a number of built-in functions to perform date and time arithmetic. If an arithmetic expression subtracts one date from another (i.e., both operands are of data type DATE), the result is a number representing the number of days between the two dates.
Consider the Date Type values: Date1 = 19990923 (23SEP1999) and Date2 = 19980923 (23SEP1998). We can now apply arithmetic to the dates by simply doing the following:
Date1 – Date2 evaluates to 365. Because the numbers are Date Types, ZIM equates to Date1 to 19990923 and Date2 to 19980923. If the same calculation was performed with INT Data Types the result would be 10,000.
If you add (subtract) a value that is not a date to (from) a date, the result is a date equal to the date operand plus (minus) the number of DAYS indicated by the non-date operand.
Date1 - 100 equates to 19990923 - 100, but evaluates to 19990615 (15Jun1999 - not 19990823) Date1 + 100 equates to 19990923 + 100, but evaluates to 20000101 (1Jan2000- not 19991023)
You can covert a Number Type value to do a Date Type value by using $todate().
If you use dates in any other type of operation, the dates are treated as numbers:
Date1/100 equates to 19990923/100, and evaluates to 199909.


Kakuro- vol 1
Play the kakuro diversion. The same digit will never rehash inside an expression. In the event that you include the digits in an expression, the entirety will be the number demonstrated in the hint. Pieces of information are indicated on the left and right sides of "over" words, and on the top and base sides of "down" words.click on the numbers in the upper right piece of the screen to choose the number. Click on a vacant box to compose the number. Click on a past composed number to erase it.


Although interest in numbers is as old as civilization itself, much about them is still not understood, and some of the oldest and most elementary sounding problems concerning them are still unsolved. A peculiarity of the number theory is that while its major theorems can often be stated in terms that anyone can understand, their proofs – where they exist – require deep, complex mathematics. Despite great advances made in mathematics over the last forty centuries, it is crystal-clear that mathematicians are nowhere close to understanding the integers, let alone other kinds of numbers.
Can numbers be finally conquered? It appears that it will take one million years at least before even prime numbers are finally understood! One undoubtedly comes to the conclusion that ‘the world of numbers is really fascinating.
JKUAT invites staff, students and the general public to a public lecture by Professor Surindar M. Uppal [B.A. (Hons.), M.A., B.T., (Punjab), Ph.D., (Kenyatta.), EBS (Kenya) ] of Department of Pure and Applied Mathematics on the topic ‘The World Of Numbers is Really Fascinating!’ to be held on Thursday, 31st March 2016, 1400hrs – 1600hrs at New Science Theatre II, JKUAT, Main Campus – JUJA


The Greatest Common Factor (GCF) is a mathematical concept this holds significant importance, but not only for students but also for math fans. Understanding how to find the GCF successfully can enhance problem-solving possibilities and simplify mathematical functions. In this article, we will explore different techniques and shortcuts that can assist math enthusiasts find the GCF swiftly and effectively.
Knowing the GCF
The GCF, also called the Greatest Common Divisor (GCD), represents the largest number that might evenly divide two or more integers without leaving a remainging. It is a fundamental concept throughout number theory and is included in various mathematical applications.
Processes for Finding GCF
Prime Factorization: This method involves breaking down the numbers into their prime aspects. By identifying common leading factors and multiplying them all, you can find the GCF.
Rating Factors: For smaller details, manually listing the reasons of each number and figuring out the common factors can be a simple approach.
Prime Numbers Short cut: If you’re dealing with two reasonably prime numbers (numbers that are fitted with no common factors except for 1), the GCF is definitely 1 .
Using the Euclidean Criteria: This algorithm https://www.azionepr.com/forum/ask-anything/writing-service provides an effective way to find the GCF connected with two numbers. It involves successive division until a remainging of 0 is reached, and the divisor at that phase becomes the GCF.
Artistic Aids and Diagrams
Math enthusiasts often find it helpful to use visual aids and also diagrams when finding the GCF. These aids can provide a precise and structured approach to determine common factors and utnost factorization. Tools like consideration trees and Venn drawings can aid in the process.
Applications of Useful GCF Calculation
Efficient GCF calculation techniques have apps in various mathematical areas:
Streamlining Fractions: When simplifying fractions, finding the GCF of the numerator and denominator is crucial to lower them to their simplest variety.
Algebraic Manipulations: In algebra, simplifying expressions often will require factoring out the GCF on the terms.
Solving Equations: Seeking the GCF of coefficients for equations can help in handling algebraic equations more efficiently.
Cutting corners for Common GCFs
There are many common GCF values the fact that math enthusiasts should remember to expedite calculations. Some of these incorporate:
GCF of 1 and Several: The GCF of 1 and any number is always 1 .
GCF of a Number and On its own: The GCF of a quantity and itself is the amount.
Even and Odd Amounts: The GCF of an perhaps even and an odd number will be 1 .
Multiples of the Same Telephone number: The GCF of multiples of the same number is that quantity.
Online Tools and Information
In the digital age, mathmatical enthusiasts can benefit from a plethora of on the web tools and resources that will help find the GCF. Sites and apps offer GCF calculators, step-by-step explanations, in addition to practice exercises to enhance GCF-finding skills.
For math enthusiasts, mastering the skill of finding the Greatest Common Consideration is not only intellectually rewarding and also immensely practical. It streeamlines mathematical operations, aids in problem-solving, and can be applied in various statistical contexts. By utilizing techniques, links, and online resources, math fanatics can become more proficient in finding the GCF efficiently, ultimately improving upon their mathematical prowess in addition to analytical abilities.


How Gardening Helps Children To Learn Math - 10 Facts
How Gardening Helps
Children To Learn Math - 10 Facts
Using garden to teach math make
the subject more easy, engaging and interesting to the children. It provides
them fun experience that they will remember.
(1) Addition and Subtraction -
Children can count the plants in
two different garden beds and then add the numbers together. If some of the
plants die, then make it into a subtraction problem. They can count seeds to
sow in each row or area. It will be lifelong lessons that they will carry to
(2) Comparing Sizes -
Children can compare sizes of
plants, fruits, vegetable or flowers. While walking in the garden. Arranging
them in order from smallest to biggest or biggest to smallest.
(3) Multiplication and Division -
Children can do multiplication
like if they want to have five lemon plants and they need to plant three seeds
in each hole, then how many seeds do they need to have? Second question may be
like if each tomato plant produces about twenty tomatoes, how many plants do we
need to two hundred tomatoes? Children can use multiplication to quickly count
plants fruits, vegetables and flowers. Once children get in the habit of posing
questions like this, I am sure you will think of many more!
(4) Calendar Skill -
Sit down with a calendar and
seeds with your child, Mark the date when you can plant the seeds. Then mark
the date when you will be able to harvest. You may tell them about how many
days in a week and in a month. Children can make a chart as a garden project.
(5) Learning Measurement –
Measuring the area of a space, it
maybe your balcony or inside the home, they will learn about planning of how
many plants they can grow in specific space, how far apart they need to plant
or sow, measuring the distance between them.
(6) Basic geometry –
Basic of geometry can be useful
as children will learn shapes and design of the garden.
(7) Algebra formula –
Such mathematics used in the
garden to calculate the correct amount of fertilizer to add for the plants.
They can calculate the volume of soil needed for a plant by calculating
Children can learn about fraction
like how much of each bed a plant takes. Example Arun and Arjun are planting a
vegetable garden. To help, their mother has divided the plot into 12 smaller
rectangular plots. Arun and Arjun decide plant tomatoes so they plant 1/3 of
the garden as tomatoes, they plant half as many peppers they plant 2/24 onions
They also plant three times more lettuce than onions They plant the rest in
(9) Graphing of the Garden –
Gardens are a great inspiration
for practicing graphing. Bar graphs are great for showing how many of each type
of fruits and vegetables you can grow in garden. You can count, compare and contrast.
You can transfer this in pie chart.
(10) Money & Finance-
Children can sell extra fruit and
vegetables. Children can learn pricing, adding up the cost, making change etc.
I hope this is the list of ways
we practice math in garden! What else would you include.


D. S. Yershov and S. M. LaValle. Simplicial Dijkstra and A* Algorithms for Optimal Feedback Planning. Proceedings of the IEEE International Conference on Intelligent Robots and Systems (IROS), 2011. [pdf]
This paper considers the Euclidean shortest path problem among obstacles in Rn. Adaptations of Dijkstra’s and A* algorithms are introduced that compute the approximate cost-to-go function over a simplicial complex embedded in the free space. Interpolation methods are carefully designed and analyzed so that they are proven to converge numerically to the optimal cost-to-go function. As the result, the computed function produces approximately optimal trajectories. The methods are implemented and demonstrated on 2D and 3D examples. As expected, the simplicial A* algorithm significantly improves performance over the simplicial Dijkstra’s algorithm.


Wird wenn sie spiel um die geld spielgeld im casino novoline casino stargames spiel um die geld casino spiele mit echtgeld poker spielen online kostenlos. Durchschläge der sich zwar casino online free bonus das spiel um die geld . online spielen mit geld app casino echtgeld casino guide freispiele verdienen sie. Casinos spielen sich selbst zum reise ein jahr dann. Betfilter ein . casino online spielen echtgeld poker geld verdienen spielautomat roulette Angabe der. Well believe it or not, you will! Originally you know only the magnitudes N , N, N, and N and the orientations angles 50, 70, 30, and 15 degrees of the four forces. Certainly, some of you are reading this website and asking yourself what in the world are these people thinking putting on an unforgettable, overnight road-trip with 11 of my closest friends. Apart from the difficulty of realizing which forces are acting on a given body and what can be said about each of these forces much confusion arises from some sign conventions which are unfortunately necessary. The concept of orthogonal components we looked at in the preceeding chapters will be employed again, but the direction of a force in 3-D is harder to describe and therefore the calculations of the component of a 3-D force is a little bit more involved. The first determines the resultant of up to 10 forces , the second program calculates that force which is necessary to hold a body in equilibrium against up to 10 forces of your choice. If the labels F 1 , F 2 , F 3 , and F 4 are not given, you must label them. D of a body is a rough sketch of a body which includes ALL forces acting on that body from the outside. Originally you know only the magnitudes N , N, N, and N and the orientations angles 50, 70, 30, and 15 degrees of the four forces. Two computer programs Using the concept of x-, y-, and z-components is also a great way to write computer programs which can tackle generalized problems. Here are my calculations for the x-components of the four forces and then the x-component of the resultant: On the other hand, to determine the components of the resultant of several forces Equation 3. Given is the magnitude of the force and the values of the angle beta and gamma. Please, do determine the value of the y-component of the resultant yourself. Also, the dashed line 0B lies in both Figures in the x-y online casino book of ra spiele kostenlos und ohne anmeldung. If it is not given, you must make a choice. To some of you it might seem silly to online echtgeld casino sizzlin hot on sign conventions. Http://www.rammert-apotheke.de/leistungen/news-detail/zurueck_zu/274521/article/safer-internet-day-2017/ direction of the force F is expressed in different ways though.


How to Win Continuously Playing Sicbo Online for online casino gambling players, there are a number agen judi evolution gaming of things you should know. If you are one of the people who really like playing online casino gambling. Surely you already know about the game of shaking the dice or better known as the Sicbo gambling game. Where the Sicbo game is a very popular game in online casino games. Therefore, online casino gambling players will usually look for ways on the internet how to win bets on this game.
There are two main types of bets for this rolling dice game, which are more commonly called big and small bets. in online Sicbo bets which include 10, 9, 8, 7, 6, 5, 4 it includes small bets and big number bets covering 17, 16, 15, 14, 13, 12, 11. you only need to add the sum of 3 numbers on the three dice.
For example, if the three dice that come out are 2, 3 and 4. Then the total number of dice is small because the value of the number is 9. And for big bets, if the value that comes out on the three dice is 11 to 17. So you can be sure that the player will win the game or bet. There are also bets which are similar but not the same namely Even and Odd bets. And this bet is also the same as the small bet too.
Even odd bets are also daftar casino evolution gaming widely played in online Sicbo dice games. How to play it is also very easy, you only need to guess the total value of the numbers that come out even or odd. For example, if the sum of the three numbers is 17, 15, 13, 11, 9, 7, 5 then it is an odd bet. and for values 4, 6, 8, 10, 12, 14, 16 are Even bets. For Odd Even bets, the winning player will be paid 1: 1 or the equivalent of the bet amount placed. Very easy, right? Are you interested in trying big small or even odd bets on Sicbo betting?
There is also a number bet
There is also a number bet where you can choose what number will appear from the three dice. You can choose from numbers 1, 2, 3, 4, 5 and 6. Number bets are very easy and easy to understand, you only guess one number from the three dice. If one of the numbers you place, you will win and will be paid 1: 1 of the bet amount. But if there are two or more same numbers at the same time you put it, then the payout will be double or triple.
Some tips so that you situs judi evolution gaming always play Sico, first of all you have to play casually and calmly. Look at the previous sicbo results board, which one comes out more often. Big, Small or it could be more even or odd outputs. Because the sicbo game is a dice game, the game will often always go with the flow.
Try to stay calm and always watch the market numbers that come out in the previous sicbo game. Usually you will easily find out which market numbers appear more often. Or you can also learn from articles that are widely circulating on the internet. The information provided from the internet is overwhelming. Even a lot of information that you don’t know before. Take articles from authors who provide many lessons on how to play Sicbo games at casinos to better understand them.
Feeling in each game is also very influential. Then you have to rely on your feeling which is more accurate and best. Generally Sicbo players also tend to play with their feelings, Feeling is sometimes very helpful if we are confused about choosing. Moreover, this feeling is also suitable for use in Sicbo gambling games. Sometimes we can guess what numbers will appear later when the dice are rolled.


Letts Make It Easy English And Maths Ages 3-5
About this deal
With quick tests and activities, this early learning book helps support the National Curriculum and is suitable for children aged 8-9 years. Read more about the condition New: A new, unread, unused book in perfect condition with no missing or damaged pages. Including a 64 page combination of activities, examples and illustrations, this English and maths activity book makes learning more enjoyable and engaging. Edges The collective of the top, fore and bottom edges of the text block of the book, being that part of the edges of the pages of a.
To calculate the overall star rating and percentage breakdown by star, we don’t use a simple average.This fun and colourful series follows the Key Stage 1 national curriculum to help strengthen your child's knowledge and understanding of key literacy and numeracy skills at home. My younger daughter whom I purchased this book for was always asking to do homework while my older child was doing school homework.
Then two handy workbooks let you preview test formats and try out practice tests so that you don’t freeze up on the big day. This fun and colourful series follows the national curriculum to help strengthen your child's knowledge and understanding of key literacy and numeracy skills at home. Watch as they gain confidence, tackle challenges with ease, and unleash their inner mathematical genius with just 5 minutes a day! This fun series follows Key Stage 1 National Curriculum to help stregthen you childs knowledge and understanding of key literacy and mathematics skills at home. I purchased this book based on a gift received to my older child for ages 6 -7 and the relevance of the topics in these books work side by side with the curriculum being used in my child's school.With just 5 minutes a day, they can build speed, accuracy, and a solid foundation in mathematics, leading them to become a math ninja in no time! The Letts Maths in 5 Minutes a Day Age 7-8 is absolutely perfect for children in Year 3 studying the national curriculum in England.


There are several types of poker, but Texas Hold’Em is the most popular. In each round, players must make an ante, or “buy in” bet, to participate. This is typically a small, one-dollar or five-dollar bet. The dealer then deals two cards to each player. Players then decide how much to bet by either raising their hand, folding, or matching the bet of the other player.
Rules of poker
When playing poker, you should follow the rules of the game. A few of these are as follows: 1. No raising or calling during your turn. 2. If you fail to call your “time,” you lose your right to act. 3. If you have more than one player, it is illegal to act against more than one player.
The first step in playing poker is to decide what hand is better than the others. You may do this by checking your cards. You can also check if no one else is betting. After that, you can raise or match the last bet made by another player.
Probability of winning
When playing poker, probabilities and odds are very important factors. As with any game, the higher your skills and knowledge, the greater your chances of winning. However, before you can start to apply these concepts to your poker play, you should learn about the various types of probabilities and odds. This will help you to calculate the amount of money you can expect to win.
One of the most important aspects of poker probability is the number of cards in a hand. In general, a hand can be composed of a minimum of five cards. However, some types of hands are dealt differently. High card hands, for example, are not dealt the same way as low card hands. In order to calculate high-card hand probabilities, you need to know the number of cards in each hand.
Probability of getting a royal flush
The probability of getting a royal flush in poker depends on how many cards you hold. If you have two cards of suit ten or higher, you are 25.6 percent more likely to get the royal flush than if you only hold one card of suit ten. However, this does not mean you will always get a royal flush. You can increase your odds of making the flush by taking the proper strategy.
The best five-card hand in poker is a royal flush. This is the ultimate poker hand, but it is not likely to happen very often. The odds of making a royal flush in Texas Hold’em are one in every 6,498,960 hands. That means that you have only a 0.00139% chance of getting a royal flush, a figure that is ten times less than the odds of making a straight flush.
Probability of getting a straight flush
The probability of getting a straight flush in poker is the number of cards in a sequence that all have the same suit. There are nine possible straight flush hands per regulation 52-card deck. This makes the probability of getting a straight flush one in 2,598,960 hands. This number is based on a mathematical formula known as combinatorics, which is the study of counting. While the probability of getting a straight flush is easy to calculate, the probability of getting a royal flush is more complex.
The probability of getting a straight flush is very low for the players holding suited hole cards. However, when there are two consecutive suited cards in a row, the odds of getting a straight flush increase to 4.25%. In such cases, building a straight flush with two hole cards is better than building it with a single hole card. A straight flush can be made with four or five consecutive suited cards. This is known as a straight flush hand and can include hands like KQJT9 (king high straight flush), JT987 (jack-high straight flush), and A2345 (five-high straight flush).
Probability of getting a royal flush in Texas hold’em
The probability of getting a royal flush in Texas Hold’em depends on several factors. First, there are 1,326 possible combinations of five cards. Of these, six are aces. As a result, the probability of getting a royal flush is one in 30940. Another factor is how many players are in the game. A game with more players has lower odds of winning.
The probability of getting a royal flush is about one in 3600 hands in a full-ring table. However, in real-life, the chance is much lower. For example, some players fold QTs before the flop, so the actual odds of hitting a royal flush are lower than these numbers. However, if you know that you can hit a royal flush, you should try to bet all your chips.


A number of the questions have bonuses. Then, once you show the answer, you return and pick another question. Every point is going to have an X-Coordinate and a Y-coordinate.
The quantities of questions can fluctuate according to timing and the degree of your students. There are typically many methods to address an issue. Triangle problems which include a proper angle are possibly the most frequent geometric math challenge that we’re most likely to see in real life.
Pythagoras Theorem worksheets with answers are readily available and you may make use of these worksheets to have a very good grip of the Theorem. Pythagoras is considered to have died at the time of about 75 decades, in about 495 BC. Pythagorean Theorem is among the most fundamental theorems in mathematics and it defines the connection between the 3 sides of an ideal angled triangle.
Pythagoras, a famed mathematician, developed the next theorem to be employed on righttriangles to get a missing side length. Geometry is an immense portion of our world. Employing https://writing.wisc.edu/Handbook/PlanResearchPaper.html the fifth and sixth sites, compare the 2 biographies of Pythagoras.
This post comprises a lengthy collection of ideas for Pythagorean Theorem. The worksheet contains questions linked to the Pythagorean theorem. Request volunteers to explain their comprehension of the Theorem.
It’s not essential to compute the area for the aims of this proof, however. Order top-notch essay at this time and certified specialists will do their very best to supply you with higher quality at fair price. It’s great to possess the answers or be ready with the answer sheet.
As a consequence, such students search for the best essay help to make sure that their project is going to be produced at the maximal level in agreement with all academic standards. Every finding, writing and contribution is going to be credited to the genuine author. This video gives an excellent explanation of the way to do this kind of question.
You might want to understand how to make an origami boat all on your own before giving the lesson. Whatever makes math cool is excellent. Let’s start by taking a peek at an example where we should find the hypotenuse.
Most 7th and 8th graders appear to appreciate the ridiculousness in these types of videos. Students adore the battle part. The kids can excel in it with the assistance of this simple worksheet.
Diagrams permit you to point out relationships within an idea. As triangle can be labelled in many distinctive ways it is most likely best to bear in mind the theorem by momorising the very first diagram above. Still require help utilizing the pythagorean theorem.
Students would search for patterns to observe when the theorem works. The differential equation implies that the theorem is because of relative alterations and its derivation is almost equivalent to computing a line integral. Use the seventh website to demonstrate the way the theorem works.
The Do’s and Don’ts of Pythagoras Theorem Project
This circle is known as the circumcircle of the triangle. That’s the equation you use whenever you’re looking for the unknown side of a perfect triangle, and it’s what I’ll demonstrate on the attached exhibit. The rest of The side is known as the perpendicular.
To utilize Pythagoras, we must know AC and CD. Find the duration of EF in the event the amount of OP is 6 cm. The very first proof starts off as rectangle and afterward is separated into three triangles that individually include a suitable angle.
Due to their angles it’s simpler to obtain the hypotenuse or the legs in these proper triangles than in the other right triangles. Within this lesson we take a look at a unique measuring rule for Right angled triangles. The Conjecture they are pursuing may be The region of the semi-circle on the hypotenuse of a perfect angled triangle is equivalent to the sum of the regions of the semi-circles on both of the other sides.
Actually there are absolutely hundreds of proofs. Students want to observe the geometric connections too. The students will produce origami paper boats.
Pythagoras Theorem Project – the Story
We will label both of the other sides a and b. Pythagoras Theorem may be used to fix the problems step-by-step while we know the duration of two sides of an ideal angled triangle and we must get the distance of the third side. The duration of a vector can be measured in various ways, but we are likely to use Euclidean distance, also called the L norm.
’X’ is the duration of hypotenuse since it’s opposite side of the proper angle. Locate the distance of a diagonal. As an example, find the distance of the hypotenuse for this perfect triangle.
Students are then going to be led to create the a variety of squares utilizing the colored graph paper. This geometry was made to allow children the chance to practice important geometry abilities. In addition, the worksheet will offer you a chance to review the knowledge associated with the several types of triangles.
After that the squares will start to overlap but the indexing algorithm will nonetheless apply as more iterations are finished. Then using the aforementioned formula, you may easily figure out the distance. Again, calculators shouldn’t be used.
Pythagoras Theorem Project at a Glance
It will amaze you the number of tools you may enhance your teacher tool box if you try only one thing at one time. This may be a good connection as it is a hands-on” activity. The next assignment is going to be a little more complicated.


1965T5090 Cube Sundial, 1750-1800 Manufacturer: I G Kleininger
* Pinto Collection, Purchased from Edward H Pinto, 1965. 1965T5090 Cube Sundial, 1750-1800 Manufacturer: J G Kleininger This cube sundial was made by J.G. Kleininger, a well-known maker of mathematical and scientific instruments in the second half of the 18th century. His work is represented in many museum collections. It is adjustable on a turned beechwood stand, and has printed paper dials to each surface of the cube.


8 Tips To Improve Your Math Grades If You’re Underperforming
All math courses follow a prescribed order, as each subject is based on the previous one. If you’re having trouble with a particular topic, work on it until you understand and resolve it. Don’t skip several topics, as this can hinder your progress along the way.
The end of the course will be more difficult, so meet your study group more often as the lessons become more involved. Also, think of ways to use the math concepts you study in class outside of class. For example, add numbers that relate to your budget, instead of just adding random numbers, to make learning math skills more interesting. Students who struggle with math will develop a habit of avoidance and procrastination when it comes to doing their math homework and studying for exams. Unfortunately, postponing work only leads to more complications. The need to rush to work or force the student to stay up late exacerbates the stress of math homework, leading to arguments between children and their parents.
Children use early math skills during their daily routines and activities. This is good news, because these skills are important to be ready for school. But early math doesn’t mean you pull out the calculator during playtime. Even before entering school, most children develop an understanding of addition and subtraction through daily interactions. After Thomas shares one, he sees that he has one car left (Bowman, Donovan, & Burns, 2001, p. 201).
Therefore, students practice math skills in a real environment. For example, when you learn concepts about the area and outline, you can draw geometric shapes on paper and assign the necessary values to the diagram. You can then use this diagram and fix the problem using the given formula. This is one of the best ways to improve math skills to achieve excellent success in math-related fields such as engineering and architecture. Do you remember those practice tests you took to prepare for the SAT or ACT?
Some students need more time to develop the problem-solving skills that math requires. Others may need to revise concepts from the past before moving forward. Because of the way math is structured, it’s best to take each year step by step, lesson by lesson. Mathnasium of Tallahassee, based in Banerman Crossings, teaches math in a way that makes sense for elementary, middle, and high school students. Before an action plan can be developed, it is necessary to identify what affects a student’s performance in mathematics.
You may remember complaining to your school’s math teacher, “When am I going to use these things?” The answer is: very often, actually! Math is important in everyday life because it helps you count bills, improve your cognition, and even bake better pies. Here are some ways math skills will help you in your daily life. 2) Work on sample problems and check your answers to practice with each lesson. The whole premise of the DVD series is “learning by example” and is simply the easiest way to learn math. After you’ve watched the section on the DVD and read the section in your textbook, start using examples from the end of the chapter.
Master the fundamental concepts of algebra, which are essential tools for high school and college-level math, science, and engineering courses. Math is useful in many situations, from college entrance exams to calculating home mortgages. Excellent math skills can also open doors to careers in data science A legitimate website to do my online class and analysis, computer programming, artificial intelligence and more. Check out these 9 online math courses to lay your groundwork and visit edX to find additional math courses for students of all levels. As a general rule, the more challenging the material is, the more time you have to spend on it.
Mathematics is crucial in terms of everyday life, as well as in the future career and choice of job. Anyone can improve math skills with a little effort and time spent studying. We’ve put together helpful tips and resources that will dramatically improve your performance. In addition, students practice problem solving in clubs and activities, including the Investment Club, the Chess Club and the Science Olympiad.
Yes, it can sometimes be helpful to remember the steps to solve a particular problem. The point is that such memorization is not a flexible skill or if the problem changes slightly, you can no longer solve it. Therefore, to know what concepts are behind the problem and solution of mathematics and what the logic is. Improving mathematical skills means gaining a better understanding of the crucial logic of this science.


Coen is just 12-years-old but he can do Year 11 maths
COEN Jones isn't even a teenager yet, but he's studying well beyond his years.
The Cathedral College maths whiz is in Year 8, but he's studying maths at a Year 11 level.
But for Coen, 12, maths is just what he does best.
"I find it (maths) interesting, I really like doing chance and data in class," Coen said.
"I think about sequencing a lot, and sometimes I can't get maths out of my head; I just can't switch it off."
His love for maths has paid off after Coen entered the Australian Mathematics Competition.
After taking the maths test, Coen picked up a prize award which is given to the top 0.3% of students in the competition.
And he won a prudence award, for having the highest number of consecutive answers right, which was 17 in his case.
Coen was excited to get the awards for his work.
While maths is a main interest of Coen's, he's also a keen musician.
Along with studying Year 11 MathsB, he's picked up three instruments over four years, which have come easily to him.
"I play the trombone, guitar and trumpet; but music is essentially maths," Coen explained.
"With music I follow patterns and sequences."
The student is hoping to one day turn his love of maths into a career and become a civil engineer.
- Lisa Benoit


How to play SA Lotto
Playing this game is easy. You need six numbers from 1 to 52. Winning Lotto numbers are being drawn every Wednesday and Saturday at 21:00.
- You need a Lotto bet slip, find it at your nearest Lotto retailer.
- Use a pencil or a pen to choose six numbers from 1 to 52 on as many boards as you wish.
- Take your Betslip to a cashier and make your payment – R5 for every one ticket per draw.
- You will get a ticket with chosen numbers, and you can sign it at the back.
- Check winning numbers on this site, and don’t throw away a ticket! Always double check numbers from different sources (tv, newspaper, or official Ithuba site: https://www.nationallottery.co.za/results/lotto/).
Lotto prizes and odds
Prizes may vary in each draw. They depend on the fact if the jackpot was won and a number of winning players in the draw. Also, it is connected with an amount of sold tickets before the specific draw. Although, the prize for matching three numbers is always guaranteed and fixed. If you match 3 of 6 numbers, you get an R50 prize. If somebody hit the jackpot, then the share of the prize pool is quite similar to shown below in the table.
|Share of prize pool
|Odds of winning
|1 in 20,358,520
|5/6 + Bonus Ball
|1 in 3,393,087
|1 in 75,402
|4/6 + Bonus Ball
|1 in 30,161
|1 in 1,371
|3/6 + Bonus Ball
|1 in 1,028
|fixed R 50
|1 in 72
|2/6 + Bonus Ball
|fixed R 20
|1 in 96
If you want to play the lottery, you need to know what are the odds of winning the jackpot after matching all six results of Lotto. Also, what are the odds of winning smaller prizes? To win the jackpot, you must defeat about 20 million possibilities (number of combinations). That means that one in approximately 20 million sold tickets wins the pot! Chances are smaller than dying in a car accident. When you play, make sure that the ticket price satisfie your expectations concerning what you can win. The chances of winning the individual prize divisions are shown in the table above.
Prize payout methods
You have one year to claim the cash you won. Smaller prizes are possible to withdraw directly from your official Ithuba wallet to your bank. You can remain anonymous after the win.
Lotto prize tax
There is no additional tax to pay after claiming the lottery prize. All fees are already paid at the ticket price.
Where to watch draw online?
You can watch every draw in the local television like SABC2 (20:56). Another option is to use youtube channel located here: https://www.youtube.com/channel/UCQWsxwRUFJHNfT202GVFghQ (broadcasts added after the drawing).
Lotto jackpots and rollovers
In this lottery game, there is something we call rollover. Jackpot prize grows as long as nobody matches the 6/6 numbers and Bonus Ball. That means pool for 1st prize division is rolled over to the next Draw’s corresponding division. That provides from time to time great cash prizes opportunities.
- If there are no winners in division 2-6 then the pool rolls down to the lower division, e.g. division 3 to division 4.
- If there are no winners in division 7 (quite impossible), then the pool rolls over to division 1 of the next draw.
- Breakage from any Lotto division rolls over to the same division next draw.
How big is the jackpot?
The SA Lotto jackpot on 03.06.2021 is estimated to be R6,000,000. The minimal jackpot amount is set to R2 million. There is no upper limit.
History of South African Lotto
Ithuba is Lotto operator from June 1st, 2015. However, African Lotto game is known from the year 2000. First SA Lotto results were published after the inaugural draw on 11 March 2000 (corresponding Lotto Plus 1 results are here). The first jackpot was split between six lucky players. President Thabo Mbeki bought the first ever Lotto ticket in Cape Town few days before the draw. From then, Lotto remains the most popular game in South Africa.
Ithuba made some changes to Lotto game on August 2nd, 2017. Lotto Plus 2 as an option to the game was proposed to the public. Lotto Plus became “Lotto Plus 1”. Since then all Lotto games had new number matrix of 52 numbers instead of 49. Prizes divisions and payout amount changed. One division with fixed prize was added. Changes were made to make more and bigger jackpots.


Spring 2015 Courses
MATH 303 Linear Algebra MWF 9:25-10:30 a.m.
My research interests lie in the field of topological and symbolic dynamical systems. Recent interests have included the study of higher dimensional symbolic dynamical systems. To get an idea of how the situation becomes much more complicated in higher dimensions, see the following article (which is accessible to undergraduates):
Putting the Pieces Together: Understanding Robinson's Aperiodic Tilings,
(with A. Johnson), College Mathematics Journal 28, (1997), 172-181.
Click for some of my research papers.
Some Fun Web Math for Undergraduates:MacTutor History of Mathematics Archive
NSF Research Experiences for Undergraduates (REUs)
This summer's REU sites in Mathematics
Women in Mathematics
Graduate Programs in Mathematics
Choosing a Graduate Program
Drew University Library Journals


Irregular Hinged Tessellations? Squares and hexagons are boring. Of course they'd work nicely together to hinge. When I first 'discovered' hinged tessellations I was most interested in which irregular shapes might work (if any). I was using blocks at the time and with a little experimentation I constructed this: unpredictable and irregular shapes that voids can occupy. Adaptive methods such as Voronoi tessellation are suited to this task, because cells are determined by point distributions rather than by assuming a priori shapes. Furthermore, while Voronoi cells are convex, their tessellation into larger structures can produce arbitrary and concave ... The Official store for Nanodots by Nano Magnetics. The underlying versatility of Nanodot construction comes from two main factors; the first is the consistency in dimension of each dot, and the second is the consistency of strength.
A Tessellation (or Tiling) is when we cover a surface with a pattern of flat shapes so that there are no overlaps or gaps. Aug 29, 2017 · Tantalizing Tessellations Several years ago, I mentioned tessellations or tilings in Bee’s Needs . For that post, I focused on the regular hexagons of honeycombs, but I mentioned that squares and equilateral triangles are the other regular polygons that may be used to create a tiling. is also known as Voronoi tessellation, Voronoi decomposition or Dirichlet tessellation (in honor of Lejeune Dirichlet), that certain types of decomposition specified metric space with distance to a particular set of discrete objects in space, such as a set of discrete points. Semi-regular tessellations (or Archimedean tessellations) have two properties: They are formed by two or more types of regular polygon, each with the same side length; Each vertex has the same pattern of polygons around it. I'm super new in blender, but have a difficult task to figure out. I saw another question and its answer about how to simulate this tessellation. Eventhough the answer looked pretty precise and kind, still the way too far to follow for me. For example I could not go to the tab or menu for add bone constrain blah. Welcome to the Los Angeles Math Circle (LAMC)! Spring Session 2020 information. Effective March 15th, no in-person meetings take place due to UCLA campus policy. These irregular shapes tessellate. On square or isometric dotted paper, choose at least one of each type and show how they tessellate. Aim to cover half a side with your shape.
Tessellations have been found in real-life. Soccer balls, plaid clothing, honey combs, and brick lying are examples of tessellations. One of my favorite things as a child was a kaleidoscope. This was a toy the when you held it the light showed a tessellation and if you rotated the scope, the tessellation would change. Volumetric lighting information is commonly stored as regular or irregular clouds of point samples,called light probes. This presentation describes a new method for light probe interpolation based on a tetrahedralization of space. Light probes may be placed anywhere, with varying density to capture important high-frequency changes in lighting. Tessellations - . sets of connected discrete two-dimensional units -can be irregular or regular regular (infinitely) Solid Texture Synthesis from 2D Exemplars - . siggraph 2007 johannes kopf, chi-wing fu et al. abstract. p resent a novel
The Official store for Nanodots by Nano Magnetics. The underlying versatility of Nanodot construction comes from two main factors; the first is the consistency in dimension of each dot, and the second is the consistency of strength.
1. Create regular polygon tessellations by rotation. 2. Determine which regular polygons tessellate. 3. Create polygon tessellations by rotation. 4. Determine what conditions cause a polygon to tessellate. Materials: Computer lab or set of calculators equipped with Cabri Geometry II and a lab worksheet. Suggested Procedure: • Group students in pairs. Jun 01, 2017 · Taj tessellations. The Taj Mahal is one of the most famous monuments in India and is very popular with tourists. It was built in the 17th century and is regarded as the acme of Mughal architecture. When visiting the Taj Mahal for the first time in October last year, it struck me that the tilings used in different parts...
Provides authoritative information on the flora of Western Australia. Glossary of Botanical Terms. Sourced from the following Western Australian Herbarium publications: Flora of the Perth Region, Parts I and II (1987), Flora of the Kimberley (1992) and The Western Australian Flora - A Descriptive Catalogue (2000). The Weaire Phelan structural tessellation uses two kinds of cells, both with equal overall volume. One is an irregular dodecahedron and the second is a tetrakaidecahedron. The pentagons in both types of cells are slightly curved in order to allow perfect tessellation.
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Some Tessellations found in Nature Tessellations in nature are not mathematically precise, but rather approximate mathematical tessellations. The photographs below were taken by Robert Fathauer. The following list describes what the photograph shows. Can you describe the tessellation in the photograph? Dec 25, 2016 · How are irregular tessellations formed? start with hexagons, triangles, squares, rectangles, or other regular shapes that can be tessellated (assembled with many other identical shapes) to cover a plane with no gaps or overlaps). start adding or subtracting other shapes to one edge of that shape ... Escher (1898-1972), a Dutch artist, is best known for his work with tessellations. He derived his inspiration from the Islamic art in the Moorish Palace Alhambra in Granada, Spain (1922 and 1936). birds, and reptiles. You will be creating designs called tessellations using transformations.
This collection of geometry worksheets has all you need to know about rectangles, activities like color and trace rectangles, finding the area and perimeter of a rectangle, rectangular path length, width and diagonals, the side length of a square, area and perimeter of a square and more. Triangle Worksheets
an irregular tessellation of polygons. An orange slide is divided into As water leaves mud during drying, it confracts. The resultant stress causes the mud to crack. This structure can be modeled as an irregular tessellation of tiles with straight and curved edges. Designing and Drawing Tessellations wedges, and each of these is 'vided into
Description: Thirty activities from a variety of Web sites, coordinated with a forthcoming book by Jill Britton for Cuisenaire/Dale Seymour, Exploring Pattern: Symmetry and Tessellations (March 1999). Topics include an introduction to symmetry; symmetry in the alphabet, in flags, in quilt blocks ... See also the Mathworld Golygon page . Gömböc, a convex body in 3d with a single stable and a single unstable point of equilibrium. Placed on a flat surface, it always rights itself; it may not be a coincidence that some tortoise shells are similarly shaped. See also Wikipedia, Metafilter, New York Times .
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An irregular vertex is an internal vertex with valence number other than four. An alternative method is to combine adjacent pairs of triangles to form a single quadrilateral [9, 10]. The drawback of this method that in order to generate a mesh with good quality, many triangular faces in the initial tessellation might be left in the output mesh. In computer graphics, tessellation is used to manage datasets of polygons (sometimes called vertex sets) presenting objects in a scene and divide them into suitable structures for rendering. Especially for real-time rendering, data is tessellated into triangles, for example in OpenGL 4.0 and Direct3D 11. Tessellation is a little bit different, unless I've got my terminology mixed up. I want a fine mesh, not just convex randomly sized polies; of which those 2 actually look pretty terrible. Too many slivers. – mpen Sep 14 '09 at 17:27
To create a glide reflection tessellation modify one side of the polygon and then "flip and slide" it with an equal side (Britton, 2009). Because the sides of the polygon have to have equal sides, not all irregular polygons can tessellate this way. (Britton, 2000) Escher's tessellation that uses glide reflections and translations. (Britton, 2000) The only three regular tessellations that exist are ones that are made up of equilateral triangles, squares, and regular hexagons. The picture above on the left is an example of a regular tessellation created by triangles and hexagons. An . non-regular. tessellation. is one that is made up of figures that are irregular polygons.
Art And Mathematics:Escher And Tessellations On first thought, mathematics and art seem to be totally opposite fields of study with absolutely no connections. However, after careful consideration, the great degree of relation between these two subjects is amazing. Mathematics is the central ... Tessellation is the process of creating a 2D plane by repeating a geometric shape with no overlaps or gaps. A regular tessellation is a tessellation that covers a 2D plane with regular polygons of the same shape and size. Only three regular tessellations (composed of the hexagon, square, and triangle) exist in the Euclidean plane . An aperiodic tiling is a non-periodic tiling with the additional property that it does not contain arbitrarily large periodic patches. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. The geometric designs in Islamic art are often built on combinations of repeated squares and circles, which may be overlapped and interlaced, as can arabesques ... Irregular Polygon Tessellation
“Regular and irregular shapes explained for primary-school parents, as well as questions about shapes that children might be asked. We explain what regular and irregular shapes are and suggest mnemonics to help children remember how many sides different shapes have.
Oct 14, 2019 · Not trying to replicate this piece exactly but I do like how the triangles often meet at mid points. This was clearly handmade but I’m trying to take a crack at it in Grasshopper. I created perforations below with delaunay triangulation but it doesn’t feel as organic, I don’t quite like how the points all meet at points. It’s too clean. I have RhinoNEST and RhinoCAM Nest, both are ... Amino acid residues in protein chains are represented by C(]t atoms, thus reducing the protein three-dimensional structure to a set of points in three dimensional space. The Delaunay tessellation of a protein structure generates an aggregate of space-filling irregular tetrahedra, or Delaunay simplices.
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Maxmind errorNext, students can warm up to the formation of tessellations by learning about a combination of shapes, regular and irregular polygons, which will tessellate. Finally, translation, reflection, and rotation will be introduced to create a greater variety of shapes before Escher style tessellations are presented to inspire students. The tiles don’t resemble simple shapes at all (more than 7 sides or contains many irregular curved sections). The tessellation demonstrates a high level of sophistication. Each tile consists of 5 to 7 sides. Some of the sides may have curved sections. Jan 08, 2015 · Today we are making our very own triangle puzzle to go along with Mouse Shapes, by Ellen Stoll Walsh!. This triangle puzzle is actually called a tessellation. A tessellation is a pattern of any identical shapes that fit neatly together to cover an area without gaps or overlapping. Aug 03, 2013 · Tessellations 31 Jul 2013. ... Deane shows how the volume of an irregular container can be calculated using a ruler. Great prompt for a problem solving activity. Symmetry Sheet 1 (Ian Mason) PDF - Sheet 2 (Ian Mason) PDF. Symmetry Patterns (Emily Corble) Lines of Symmetry (Kate Warner) Symmetry (Dylan McCarthy) DOC. Flag Symmetry (Sarah Shardlow) PDF. Tessellating Shapes (Rob Burton) Reflection Grids (Louise Bussell) DOC. Shape Sequences (Caroline Payne) DOC. Reflections in a Mirror Line (Ali McNamara) DOC.
Therefore, there are only three regular tessellations (composed of the hexagon, square, and triangle), illustrated above (Ghyka 1977, p. 76; Williams 1979, p. 36; Wells 1991, p. 213). There do not exist any regular star polygon tessellations in the plane. Regular tessellations of the sphere by spherical triangles are called triangular symmetry ... Transformation, tessellation and symmetry – rotational symmetry. A shape has rotational symmetry if it looks the same in different positions when turned from a central point. This shape has rotational symmetry of order 3. This means it looks exactly the same in 3 different positions. Another relevant type of tessellation is a ‘flagstone’ tessellation; Lang also worked out an algorithm to produce one of these from a spiderweb. Polygons in a flagstone tessellation are designed to end up entirely on top after creases are folded, requiring at least four creases between each polygon if flat-folded.
Therefore, there are only three regular tessellations (composed of the hexagon, square, and triangle), illustrated above (Ghyka 1977, p. 76; Williams 1979, p. 36; Wells 1991, p. 213). There do not exist any regular star polygon tessellations in the plane. Regular tessellations of the sphere by spherical triangles are called triangular symmetry ...
How regular shapes tessellate Various grids and patterns Make tessellations online Colour in regular tessellations Draw irregular tessellations Square grid Triangle grid Escher-style Examples of tessellations Optical illusions - mostly square grid Triangle grid Escher-style General information For teachers Links to other websites Anonymous Sun Feb 9 02:28:43 2020 No. 724221 >>724219 Good materials, correct lighting, yes both are essential. But he's compositing the shit out of his image. Blur, noise and grain, bloom, and seemingly half resolutions, you're able to get away with a lot more when half the picture is edited whether inrender or through photoshop. In geometrical terminology a tessellation is a pattern resulting from the arrangement of regular polygons to cover a plane without any interstices (gaps) or overlapping. The patterns are usually repeating.
May 07, 2017 · Quick introduction to Tessellate operation in Tissue add-on for Blender. Tessellate allow to easily create copies of an object on the faces of an other object. The difference from Dupli-Faces is ...


11:00AM, Tuesday 08 August 2017
A high-flying former James Elliman Academy pupil and Mensa member returned to his old primary school to present an award to two talented maths students.
Jasamrit Rahala, 12, who left James Elliman Academy for Herschel Grammar School in 2015, paid a visit to his old primary school’s annual prize day on Tuesday, July 18.
Jasamrit, who is due to start a scholarship at Eton College in September, presented the Jasamrit Rahala Maths Shield to the school’s highest year six maths SATs achievers.
Joint winners Tayyab Nawabi and Faizan Mahmood both scored 109/110.
In a speech, Jasamrit said: “I know that today I have come to hand out an award on mathematics but this means so much more than that.
“I have re-united with the teachers that have shaped my life and helped me to persevere.”


If all tests are negative, the positive rate is zero. And its confidence interval?
Some time ago a colleague presented me a simple statistics question which, as usual, turned out to be quite interesting and intriguing. They had run 23 tests that were all negative, and they wanted to have a confidence interval for the proportion of positive outcomes. So, to put it in statistical terms, we have observations that can be 0 or 1. Each observation has a probability of being positive. In formulas
We know that the number of successes is binomially distributed, thus a sufficient statistics is and that the maximum likelihood estimator for the binomial proportion is
If the observations are all negative, the estimate for the rate is clearly zero, but what about its confidence interval? I had never been asked to estimate the confidence interval for the binomial distribution, so I was totally unprepared (shame on me!). Quite instinctively, I computed the probability to observe all 23 results negative for a given , set this to 5% and solved for . Result, 12.2%. In formula
which gives, solving for ,
In other words, what I did was to compute the highest for which I would be very surprised (5%) to see all negative outcomes. This is equivalent to being quite sure (95% sure) to observe at least one positive outcome.
My colleague had found the formula for the Clopper-Pearson interval and applied it to their case: different result. Of course, I thought: I computed the probability to observe data as extreme or more extreme than those observed for a given value of the parameter. I did a hypothesis test, not a confidence interval.
It would have been the end of the story, had I not tried this online calculator. It reports to be the 90% interval for . This was no coincidence, as the plot below shows.
In other words, for any number of tests (at least, between five and thirty) my estimate (violet points) matches the upper limit of the 90% confidence interval computed with the Clopper-Pearson method (magenta line).
library(ggplot2) library(ggthemr) ggthemr('solarized', type='outer') # computing 90% confidence interval with "exact" meaning Clopper-Pearson library(binom) cis <- binom.confint(0, 5:30, conf.level = 0.9, methods="exact") # max theta for which n all negative outcomes have probability 5% p_all_neg <- 1-0.05**(1./5:30) df <- data.frame(x=5:30, y1=cis$upper, y2=p_all_neg) p <- ggplot(df, aes(x)) + geom_line(y = df$y1, show.legend = TRUE, colour='#d33682') + geom_point(y = df$y2, show.legend = TRUE, colour='#6c71c4') + xlab("trials") + ylab(expression(theta)) + ylim(0.0, 0.5) + theme(axis.title.x = element_text(face="bold", size=18), axis.text.x = element_text(angle=0, vjust=0.0, size=14), axis.title.y = element_text(face="bold", size=18), axis.text.y = element_text(angle=0, vjust=0.0, size=14)) print(p)
Finding confidence intervals
There is a one-to-one correspondence between confidence intervals and hypothesis tests. As a matter of fact, confidence sets are found by inverting a test statistics.
Let’s start revisiting a few concepts, following the classics. We have a hypothesis for a parameter of interest $\theta$. The hypothesis says that it has a certain value
We have data and a test statistics telling us whether to reject the hypothesis or not. The acceptance region is the region of the sample space for which we do not reject at a level . In symbols
Now, for each realisation of the data , we take the values of for which the hypothesis is accepted. Then we have built a confidence set for . We define as the set in parameter
Then, is a confidence set. This follows quite immediately from the definition of acceptance region above
There are several estimators for the confidence interval of the binomial proportion. The advantage of this one is that it is exact, rather than based on the normal approximation (see the Wikipedia page linked above). The disadvantage is that it is conservative, i.e. there might be a smaller interval with the same confidence level. The estimated interval is defined as
From this definition we reconcile the fact that my estimate at 95% coincides with the Clopper-Pearson at 90%. In fact, since we are in the special case of , we can write the Clopper-Pearson as
By taking in the Clopper-Pearson estimate, we have the formula I used for my estimate.
A final observation
What is most interesting to my colleague? The hypothesis test says that those data would already exclude or higher at 5%, but the 95% interval according to Clopper-Pearson is . As we saw they are two different but intimately related things. What is more important to you depends largely on your taste. We also had the chance to underline something that is often neglected: finding an confidence interval doesn’t mean we found the smallest interval that contains the true value with probability . If you want to investigate an extreme consequence of this, you can visit the ultimate confidence intervals calculator.
Header image from Flickr


I began my teaching career in the fall of 2004. I taught at Lincoln-Way Central for five years and then moved to Lincoln-Way West when it opened in 2009. I have taught Computer Programming (C++), Algebra AB, Algebra 1, Plane Geometry, Algebra 2, Pre-Calculus, Honors Pre-Calculus, Semester Statistics, AP Statistics, AP Calculus AB, AP Calculus BC, and AP Computer Science (Java). While at Lincoln-Way, I have coached freshman football and Mathletes as well as sponsored Intramurals and Student Council. I also taught for five years for Sylvan Learning Centers - three years in Frankfort, IL and two more in Merrillville, IN.
I earned my Bachelor's Degree in Mathematics from the University of Illinois at Urbana-Champaign in 2002. I stayed for two more years and earned my Master's in Education in 2004. I did my student teaching at Champaign Central High School and at Jefferson Middle School. Before college, I graduated from Lincoln-Way High School in 1998 and was a member of the 1997 State Champion Football team. I was also a part of Mu Alpha Theta and Pi Sigma Pi.


The mathematical patterns in the physical structure of spider silk show similarities to those in classical music composition, according to a new U.S. study.
Researchers at Massachusetts Institute of Technology (MIT) have revealed a structure-function relationship in two seemingly disparate fields—the composition of proteins and musical riffs—that may help engineers design new materials and even infrastructures.
The team used a branch of mathematics called category theory to create ontology logs or “ologs” by looking at the items’ primary building blocks: amino acids and sound waves. Ologs allow a system’s properties to be categorized abstractly, and reveal the inherent relationships between structure and function.
“The seemingly incredible gap between spider silk and music is no wider than the gap between the two disparate mathematical fields of geometry—think of triangles and spheres—and algebra, which uses variables and equations,” said study co-author David Spivak in a press release.
“Yet category theory’s first success—in the 1940s—was to express a rigorous mathematical analogy between these two domains and to use it to prove new theorems about complex geometric shapes by importing existing theorems from algebra.”
The olog allows scientists to compile information about how materials function in a mathematically rigorous way, and pinpoint patterns that are found universally in a broad variety of materials.
“There is mounting evidence that similar patterns of material features at the nanoscale, such as clusters of hydrogen bonds or hierarchical structures, govern the behavior of materials in the natural environment, yet we couldn’t mathematically show the analogy between different materials,” said Markus J. Buehler of the Department of Civil and Environmental Engineering (CEE) in the release.
Interestingly, even when mistakes occur in the patterns, the overall harmonic sequence and function is generally unaffected.
“The fact that a spider’s thread is robust enough to avoid catastrophic failure even when a defect is present can be explained by the very distinct material makeup of spider silk fibers,” said study co-author Tristan Giesa in the release.
“It’s exciting to see that music theoreticians observed the same phenomenon in their field, probably without any knowledge of the concept of damage tolerance in materials,” he continued.
“Deleting single chords from a harmonic sequence often has only a minor effect on the harmonic quality of the whole sequence.”
The findings were published in the December issue of the journal BioNanoScience.


It’s income tax season again. OK – W2 season, as many here in Winter Haven, Florida will wait until that fateful April deadline to file their taxes. One of the bright spots we home owners get to look forward to around this time of year are the deductions we get to claim.
However, like most IRS-related items, the exact nature of the mortgage interest and real estate tax deductions tends to be a bit foggy. So, as your friendly neighborhood Florida home loans specialist, allow me to clear things up a bit:
Homeowners are entitled to two basic home-related tax deductions — the first is for the amount of annual mortgage interest paid, and the second is for real estate tax bills paid. This said, not all Winter Haven area homeowners are eligible for these deductions.
Two key things that might exclude you from taking these deductions are total amount you borrowed to buy your Winter Have, FL area home and whether the home is classified as a primary or secondary residence.
The official IRS publication relating to these two deductions is filled with notes and explanations but, in general, you can calculate your approximate mortgage interest tax deduction as follows:
- Add up your annual mortgage interest and real estate taxes paid
- Find your tax rate on the IRS tax bracket schedule
- Multiple your tax rate by the sum (the total from your addition problem) in step 1
This is a very simple explanation, but it will suffice for a rough estimate. Seek out one of many online mortgage calculators to assist you in this process.
Here’s an example for you to review:
Henry homeowner paid a total of $25,000 in combined mortgage interest and real estate taxes for 2008. He looked up his tax bracket using the IRS tax rate guide and determined that he is in the 28% tax bracket. Doing the math a prescribed above, he calculated his approximate IRS home-related tax deduction to be $7,000.
The availability of mortgage interest tax deductions is one reason why loan officers make reference to “after-tax mortgage rates.” An after-tax mortgage rate is the effective interest rate, post-tax code, and can be calculated using the formula below:
(After-Tax Mortgage Rate) = (Mortgage Rate) * (1 – Marginal Tax Rate)
A homeowner with a 5.5% mortgage rate will therefore have an after-tax mortgage rate of 3.96%.
Because not every homeowner is eligible for home-related deductions, and because not every homeowner should claim them, talk with your personal accountant before making any tax-related decisions.
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QuantumHermit interviewed Cohen et al on their work on using Google’s D-Wave for portfolio optimization . Following is the interview …
We were motivated by the idea of well understood and valuable challenge, financial portfolio optimization, and solve it both classically and with a quantum computer. We set our sights on a problem that was challenging classically, a universe of 40 liquid US equities with one year of historical data, and we solved it on a D-Wave quantum annealing computer. Our goal as a team is not to beat the stock market, but to help asset managers and individual investors build optimal portfolios, and improve investment productivity.
What is financial portfolio optimization? It is the art of building an investment portfolio which delivers the highest expected return for each measure of risk. The decades-old formulation is the Sharpe ratio, which divides expected return (%) by standard deviation of returns (%). Put into regular language, can we earn more profit for each unit of risk taken?
To simplify the problem and eliminate much of the guesswork of picking your expectation of market returns, or the risk free rate set by the US Treasury, we created a ratio that divides the market momentum by the standard deviation of returns. Market momentum is made up of covariances of stocks against the market for that portfolio. This gives us an effective and conservative way to build portfolios that is only based on the movements of stocks, and we call this the Chicago Quantum Ratio (CQR).
However, quantum annealing computers run off a QUBO, or a quadratic, unconstrained binary optimization problem. This is matrix mathematics that is linear…so it cannot divide a ratio. Our team’s first significant innovation was to reformulate the problem into a linear formulation, which nets portfolio variance against the expected return of the portfolio, raised to a power. This builds a metric that allows a user to find effective portfolios on or near the efficient frontier, and can be run effectively on a quantum annealing computer. We see this in figure 1.
The second significant innovation was to tune and engineer the solution to run on the D-Wave effectively so we have enough ‘valid portfolios’ to answer the question, and pick the best portfolios with confidence. We build multiple matrices to solve the problem. We apply affine transformations to shift the values of each matrix, while keeping our valid portfolios exactly accurate. Finally, we learn how to scale and apply negative and positive signs to our matrix values. These three steps allow us to maintain a binary problem, and enable the D-Wave to more often see the energy levels and solutions we want.
Let’s step back and see how we solve the problem classically.
We use brute force to evaluate every portfolio option. For 28 assets, or 2^28 portfolios, this takes a few hours on a desktop. For 32 assets, or 2^32 portfolios, this takes days on our laptop. For 40 assets, 2^40 portfolios, or 1.1 trillion portfolios, this would take a long time to complete, but we can validate the quantum results.
We use a genetic algorithm to find the one best solution, in a timeframe competitive with a quantum computer. It gave us a 3 out of 40 asset solution consistently after 80 generations of 60 solutions, and 1028 initial seeds. We modify the level of mutation to look for deeper solutions. Interestingly enough, when we seed the genetic algorithm with the D-Wave results, it came to the same answer in 2/3 of the time.
We used random sampling, a form of Monte Carlo analysis, and found good solutions, but not as good as the D-Wave system. By comparison, we ran 950M random samples against the D-Wave running 60,000 samples. To ensure the D-Wave was not giving us random solutions, we compared the averages for each portfolio size (e.g., the number of stocks to receive an even amount of investment). For solutions under 25 assets, the D-Wave had better answers (see figure 6). For the largest portfolios, random samples did better.
We also found a heuristic approach where we find portfolio ‘Allstars’ that appear most often in the best portfolios. We also find portfolio ‘Dogstars’ that appear most often in the worst portfolios. We can build larger and better portfolios by gathering and pre-selecting Allstars and avoiding Dogstars. We plan to leverage this learning, or what we see as the value of stock picking, when we run our algorithm on gate-based quantum computers.
Overall, the answers were best from the genetic algorithm (one best solution), followed by D-Wave, then random sampling. In terms of timing, the genetic algorithm was comparable to D-Wave, but was far faster than random sampling for equivalent quality answers.
Our next steps include increasing the portfolio size to 60 assets, then potentially 80 assets. This take the problem outside the scale where we can solve it classically with brute force knowing all the answers, at least without use of a supercomputer. We will also link together a synthetic annealer with a genetic algorithm, which will improve our classical speed, and give the quantum computer a tougher comparison. Finally, we will invest to improve our engineering to accelerate and improve our quantum results.
Although this work was all self-funded by the team over the course of a year, we would like to acknowledge and thank the writers, maintainers, and community contributors for Python, Numpy, Pandas, Matplotlib, Scipy and DWave Ocean, Julia and R. We also thank D-Wave Systems, Google, Slack, Anaconda, and Jupiter for the use of their tools in this research effort.
Our data was 40 US traded liquid stocks as of 1536 CT, on June 24, 2020. We have the data if other researchers would like to replicate our research.
The paper can be found here : https://arxiv.org/abs/2007.01430


As it is releasing the seventh volume, Spora has established itself to be a highly respected journal for student-driven research in mathematics, biology, and related fields. Spora's role in disseminating work that was conducted by at least one student author makes it a unique platform to expand the body of knowledge in mathematical biology. Spora welcomes submissions related to Ph.D. dissertations, master's theses, and undergraduate research projects.
"Fostering Research and Education in Mathematical Biology,"
Spora: A Journal of Biomathematics: Vol. 7, .
Available at: https://ir.library.illinoisstate.edu/spora/vol7/iss1/3


GoLang Solution For UVa Online Judge: 10139 - Factovisors
GO Solution For UVa 10139 - Factovisors. In this post we will see how we can solve this challenge in GoLang for UVa Online Judge.
The factorial function, n! is defined thus for n a non-negative integer:
0! = 1
n! = n× (n− 1)! (n > 0)
We say that a divides b if there exists an integer k such that
k × a = b
Input The input to your program consists of several lines, each containing two non-negative integers, n and m, both le...
You can find the full details of the problem Factovisors at UVa Online Judge
6 9 6 27 20 10000 20 100000 1000 1009
9 divides 6! 27 does not divide 6! 10000 divides 20! 100000 does not divide 20! 1009 does not divide 1000!
Solution: Please check the main.go snippet for the solution.
Solution originally posted at: Github by @codingsince1985


Geometry began with a study of measurement on objects' size, relative position and space on the Earth. As most of our actions take place on Earth, we need to understand geometry. In addition, geometry also provides a vigorous training on use of logic in presentation and discussion of ideas.
Basic terminologies and concepts
Here are some basic terminologies and concepts in studying geometry.
- Point - basic element of geometry which represents an object without any size. It is the abstraction of things like the tip of a needle, a pencil, a mark drawn by a pencil ...
- Line segment - a line segment is an object with no width and height but has a finite length. If you draw two distinct points (the end points) using a pencil and connect them together, the object formed is a line segment.
- Line - a line is an object with no width and height but has an infinite length. If we extend the line segment drawn in the above indefinitely, we get a line.
- Straight or curve - a line segment or line is called straight if it is constructed in a way such that the direction is not changed. Otherwise, it is called a curve.
- Ray - a ray is an object which is obtained by extending only one end point of a line segment indefinitely. The other end point is kept fixed.
- Angle - an angle is an object formed by having two rays with the same fixed end point.
The following diagram shows the objects discussed above. Can you identify them?
Exploration of different types of angle
As you move the point C or A in the above simulation, you can see that the angle \(\alpha\) changes its size. Angles are named according to their sizes. Angle size is commonly measured by degree. For a complete round (a circle), named round angle, is arbitrarily assigned to be 360 degrees, symbolically \(360^o\). For finer measurement, we define 1 degree to be composed of 60 minutes and 1 minute to be composed of 60 seconds. This is very similar to our time system.
Based on this, the following commonly named angles are defined as the size of the angle \(\alpha\) increased:
- acute angle
- right angle
- obtuse angle
- straight angle
- reflex angle
Use the computer simulation below to learn how to measure and explore the above named angles.


Science and Math Preview Day will give you a great first-hand look at all that Cedarville's Science and Math Department has to offer. You’ll spend the day interacting with faculty and students, participating in lab demonstrations, and learning more about Cedarville University.
Who: All high school students interested in Biology, Chemistry, Earth Science, Mathematics and Physics.
Where: Cedarville University
When: February 9, 2019
Cost: Free, but registration is required
Please follow this link for more registration information!


News Archives - 1998
Augsburg College student Erik C.B. Johnson wins Goldwater Scholarship
Augsburg College junior Erik C.B. Johnson, a 1995 graduate of Vermillion High School in Vermillion, S.D., was one of 316 undergraduate students nationwide in the fields of mathematics, science and engineering to earn a prestigious Goldwater scholarship for the 1998-99 academic year.
Johnson, who has a 3.98 grade point average, received a one-year scholarship that will cover the cost of tuition, fees, books and room and board up to $7,500.
The scholarship winners were selected by the Barry M. Goldwater Scholarship and Excellence in Education Foundations from more than 1,100 nominees by college and university faculties.
Johnson is the second Augsburg student in the last three years to be named a Goldwater scholar, and this year he was one of eight students from Minnesota private colleges to receive the award.
After graduating from Augsburg in May 1999, Johnson, the son of Christopher Johnson and Dr. Susan Johnson of Vermillion, S.D., plans to pursue doctorate (M.D./Ph.D.) degrees.
The federally endowed Goldwater Foundation has awarded 2,407 scholarships worth approximately $25 million since being established in 1986. The scholarship program was designed to foster and encourage outstanding students to pursue careers in the fields of mathematics, the natural sciences and engineering. Goldwater scholarships are considered the premier undergraduate awards of their kinds in these fields.
Augsburg is a private college of the liberal arts and sciences and is affiliated with the Evangelical Lutheran Church in America. Nearly 3,000 students are enrolled at the College in undergraduate day college, Weekend College and graduate programs.


Swiss scientists break a new record for calculating the constant Pi
A team of Swiss scientists beat a new absolute record in the calculation of the intriguing mathematical constant Pi. On this occasion, with the help of a supercomputer, they managed to get 62.8 billion figures, which brought them even closer to the distant infinity.
As reported by Graubuenden University of Applied Sciences in an official statement released Monday, theimpressive calculation took 108 days and nine hours.
Pi computation record throughout history
This is undoubtedly a historical milestone, but to better understand its impact, let’s review the history a bit. Even the Greek mathematician Archimedesrecognized for his contributions to the density calculation, he made his mark by being able to determine the value of Pi in an interval close to his time.
The first digits that make up the constant Pi are 3.141592653, especially useful for geometric and engineering calculations. But throughout the history of calculus, many people have been interested in getting a more accurate value for this constant. Indeed, we could say that it has become a competition in which many want to stand out.
The latest record was achieved by Emma Haruka Iwao, a Google employee, who got the closest approximation recorded up to 2019. His result gave an irrational number with 31.4 billion digits. Emma spent 121 days doing this, helping herself with more than 20 machines and the company’s cloud services.
A venture that could lead to the development of high-performance computers
Until now, the closest approximation had returned 50 trillion digits, but this time the Swiss scientists far surpassed it. The university noted in the statement that its efforts were “nearly twice as fast as the record Google set using its cloud in 2019 and 3.5 times faster than the previous world record in 2020”.
Curiously, the goal was not just to overcome previous approaches. In reality, these types of complex calculations pursue a ambitious goal which will influence the development of more sophisticated technologies with wide fields of application: high-performance computers.
An important milestone was reached with the calculation of pi at 62.8 trillion decimal places in hexadecimal notation. The final result is expected in about two weeks. So far, only the last 10 digits of the new calculation record for the constant Pi are known: 7817924264. Meanwhile, the scientists behind the feat are eagerly waiting to be registered in the Guinness Book of Records.


I used the above example using the worldwide subscription rates of 19.25/mo. Had I used the subscription rate for a single country (US) of 8.50/mo then the difference would be a lot more. The one years special would cost only SGD $5.67/month.sundaymorningstaple wrote: If you extrapolate then, unless I'm doing something wrong, I find the following.
If both are used for 10,000 per month (the limit of skype's policy) the cost of poivY would be as follows:
As per their policy of 300min/WEEK free X 52 / 12mo = 1300 free min/month. After that you pay 3.2¢/min or .032 x (10,000/mo -1,300/mo = 8,700/mo) = SGD 278.40/mo versus skype's 19.25/mo w/out discount. With the one years special skype would only cost SGD 12.83/mo
So I guess it would depend on how heavy a user you are in the long term.
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I have several students trying to accelerate through full year classes over the summer so that they can skip to the next level. One in Algebra II, and two in Geometry. One of my geometry students said today, “Does it get any harder than this?”
The only thing that’s hard about Geometry is the AMOUNT you have to know — the theorems you have to be able to just rattle off.
But this kid is FLYing. It’s fun to teach someone who is so quick with it. We have to get through 12 chapters, and I’ve only worked with him 2 weeks now and we’re almost done with chapter 4. And he GETS it. Woohoooo!


Calculate expected value of your casino bonus easily (with examples!)
Math matters. When you are looking at a sportsbook, casino or poker bonus to claim, they have conditions attached. By looking at these conditions you can quickly and easily calculate the expected value of your bonus, in order to be able to rank it against other bonuses. Bonuses on website online kladionice, for example, all list the percentage and the cash value, but to find the expected value you have to dig just a bit deeper. Let’s teach you how to do that.
To calculate the expected value of a bonus, you need 1. bonus amount, 2. wager requirement, 3. house edge. You’re actually comparing two things: the amount of money you get and the amount of money you’ll lose while playing, and are then comparing the two to see what you have left, if anything. This is the basic principle of calculating expected value of a bonus and it applies to all bonuses.
Let’s use the Bet365 casino bonus as an example.
They are offering a 100% bonus up to €100, with a rollover requirement of 15x deposit plus bonus, so 15 x 200 = €3000. You’re obviously getting €100 for free, so let’s see how much you’d lose while wagering a total of €3000 on a certain game. Bet365 have a nice little slot game in their lobby, Bermuda Triangle, and it has RTP of 96.73%, which means the house edge is 3.27%. Of course, this is the theoretical payout over an infinite number of spins and the actual RTP will vary wildly in one playing session, but we need to use the data we can get.
If you’re wagering €3000 on something with a house edge of 3.27%, you’re expected to lose 3000 x 0.0327 = €98.10. That means the expected value of your bonus is 100 – 98.10 = €1.90. That’s not much, but if you’d choose a slot game with RTP of 98.00%, or a house edge of only 2%, then you’re expected to lose €60 while meeting the rollover requirements so the expected value of your bonus is 100 – 60 = €40.
Or, if you’re playing one of our favorite slots, Ooh Aah Dracula, that has RTP of 99.00% and even lets you purchase a bonus feature for cash as opposed to waiting for it, you’re only expected to lose €30 while meeting the rollover conditions and would be left with nice €70. Bet365 don’t have this particular Barcrest slot, so we’re just using it as a mathematical example of how much more money you’d be left with if you chose a higher-payout game.
Now, an interesting wrinkle here is that Bet365 allows the bonus to be played through on baccarat with a 25% contribution, on roulette with 20% contribution, and even on blackjack with a 10% contribution – but this is actually making things worse. European roulette has a house edge of only 2.70%, which is great, but you’d have to wager 5x more on roulette than you would on slots for the purposes of this bonus, and you’d end up with a calculation that goes like this. You get €100 for free, but have to wager €15,000 on a game with a 2.70% house edge, and you’re expected to lose €405 while doing that – so the expected value of your bonus is actually negative – minus €305.
Using this same principle, you can quickly calculate the expected value of any bonus you can get, regardless of it being a casino, poker, sportsbook or bingo bonus. The only thing that matters is calculating how much money you’ll lose while meeting the rollover requirements. That’s it. When you have that, simply see if the number is larger or smaller than the bonus you’re getting.
Any advanced calculation of expected value will not only include the house edge as such, but will also include the chance of you winning, and will sometimes even take into account your bet size. For example, if you’re claiming a sportsbook bonus and have to play through your bonus on odds 1.70 and the bookmaker already has a house edge of 8% embedded in the odds, then the bookmaker will offer odds of 1.83 on two sided bets where real odds should be 2.00-2.00. That means you have a 50% chance of winning that bet but will be losing quite a bit on the vigorish.
When it comes to slot machines, they have different degrees of variance and different hit rates (percentage of spins that produce a win), and of course the overall risk is much lower if you pick a slot game that doesn’t have a high variance, as you might just catch the high-variance slot machine at the wrong time and get no wins. What you need are slots that pay regularly, small amounts, so you can claim your bonus without going too deep into negative. Lower variance also lets you play with courage, with a larger bet per spin.
We can’t possibly give an example for this, we’re not experts in probability theory! If you are, just bear in mind the hit rate counts and you want it to be high in order to decrease variance and therefore decrease the chance of bankruptcy. Further reading: Wikipedia article on Expected Value
Do calculate the expected value of your bonus each and every time you want to claim one. Pick the highest-payout game in the casino and calculate the expected value if you played through your bonus on that game alone. After doing this a few times you’ll feel as if you have control over the casino and over what is essentially a random game of chance, just because you took the available data and made sense of them. Soon you’ll discover not all bonuses were created equal, and some are just not to be touched with a ten foot pole while some are a gambler’s dream.
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Activities are important because they help children apply what they have learned. One of the best ways to teach these learners is to engage them in activities that will help them discover and enhance their skills. Thus, we have developed activities that will enhance our pupils’ learning experience.
Our activities include:
- Practical life
includes life skills to help develop independence, coordination, concentration, self-control, self-awareness, and confidence.
- Sensorial activities
allows the child to refine each of their senses: – sight – touch – smell – taste-sound and stereognostic.
- Language activities
is based on phonetic awareness. children work through specific hands-on and tactile language materials such as sandpaper letters to the moveable alphabet. We also enrich the program by adding “Fun Family Phonic”. Children can learn the language through fun ways.
- Mathematics activities
is developed with the use of concrete learning materials. The sensorial area is the preparation for mathematics. Hands-on materials are used such as number rods, number boards, spindle box and number tiles etc… each exercise builds upon another and the child gradually moves to from concrete to abstract areas such as place value, addition, subtraction, multiplication, and fractions.
allows the child to explore the natural world around them and includes:
- Geography (continents, landforms, earth layers, solar system).
- Zoology (classification, physiology of animals)
- Botany (ecology, classification, physiology of plants)
- History (time lines, using a calendar)
- Art and music
However, creativity is encouraged across all curriculum areas. We also include dramatic play into our curriculum to stimulate the children’s imagination.
To learn more about our activities, don’t hesitate to contact us today.