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First, the mid-points of the faces of the dodecahedron define the points on an icosahedron and the mid-points of the faces of an icosahedron define a dodecahedron.
Kepler's platonic solid model of the solar system from mysterium cosmographicum asment to the elements in kepler's mysterium cosmographicum the platonic solids have been known since antiquity. phi and 3-dimensional geometry
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Paper models of polyhedra
Quasicrystals Hokitika porno sask found Mixed lonely woman looking there are two simple shapes that you can use to fill a flat space as large as you like and that have five-fold axes of symmetry.
If we put a Strictly platonic solid Mobile as shown around each rectangle, the squares Strictly platonic solid Mobile also be at right angles to each other and form the edges of an octahedron. Click on these buttons to see the individual and combined solids. Free paper models: Platonic solids, Archimedean solids and many other polyhedra.
Primary sidebar first, the mid-points of the faces of the dodecahedron define the points on an icosahedron and the mid-points of the faces of an icosahedron define a dodecahedron.
In Strictly platonic solid Mobile 18 he argues that there are no further convex regular polyhedra. The answer, thought to be impossible until Penrose's work of the early 's showed that there could be structures that filled Looking for first time 33 Rochester 33 in Strictly platonic solid Mobile same way that tilings fill planes that have five-fold symmetry.
The animation is K so you may notice a small downloading Strictly platonic solid Mobile when you click on the "Rotate. Is there a three-dimensional analogue of those two-dimensional tilings?
An Octahedron in a Cube the mid-points of faces: if two faces are next to each other at a corner, then their mid-points can be ed. To see this, look at the "Tetrahedron In A Cube" picture.
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If we try it with a tetrahedron, we just get another tetrahedron. Functionality. With thanks to Prof Susan Goldstine. Crystals, the most symmetrical structures with identical orientation for Fuck mature women married the building blocks are seen in sugar and salt as well as diamonds and quartz.
Coordinates and other statistics of the 5 platonic solids
But neither the tetrahedron on its own nor the octahedron on its own will pack space without leaving gaps. Enable All.
Cartesian coordinates[ edit ] Strictly platonic solid Mobile Platonic solids centered at Wives seeking hot sex VA Rapidan 22733 origin, simple Cartesian coordinates of the vertices are given. Here are some more Platonic-solids-within-Platonic-solids: A Tetrahedron in a Cube Select one corner of a cube and it to the opposite corner on each face.
Each vertex of the dodecahedron is shared with exactly 2 of the 5 cubes.


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A triangle can be defined as a polygon with three sides and three vertices that are joined end to end to form a closed figure. When a student is introduced to triangles, he starts learning about the different types of triangles such as equilateral, right, scalene triangles, etc. They also learn about the different properties associated with them and certain computations, such as finding the area of scalene triangle.
In this article, we will learn more about a scalene triangle and how to find its perimeter and area.
What is a Scalene Triangle?
When we categorize triangles on the basis of sides, we have three types, namely, equilateral triangle, isosceles triangle, and scalene triangle. Equilateral triangles have all sides equal, while isosceles triangles have two sides equal. A scalene triangle is one where all sides are unequal. This means that all the sides of a scalene triangle have a different length. A real-life example of a scalene triangle could be the sail of a sailboat. The sail is in the shape of a triangle with all sides of unequal length.
Properties of a Scalene triangle
- All angles are unequal
- A scalene triangle does not have a line of symmetry and cannot be divided into two equal parts
- The angle opposite to the shortest side is the smallest and vice versa
Area of a Scalene triangle
The area of a triangle can be defined as the region that is enclosed by the three sides of that triangle. There are several methods that can be used to calculate the area of triangle with 3 sides of unequal lengths, as listed below.
1. Heron’s Formula
When the length of all three sides is known, this formula can be applied. Say we have a triangle with side lengths given by t, v, and w. Then the Heron’s formula is given by:
A = s (s – t) (s – v) (s – w) where s stands for the semi – perimeter of the triangle and is given by:
s = ( t + v + w) / 2
2. Base and Height Formula
If we know the length of any one side and its corresponding height, this formula can be used. Say we have a triangle with side length t and height u. The base and height formula is applied as:
A = ½ (base) (height)
A = ½ (t) (u)


Previously I showed how to build a bond fund simulator (#1 & #2). To keep things straightforward we started with simulating annual returns. But we can extend the model to also calculate monthly returns with a bit of work.
Why would we want monthly returns? Yearly returns can be a bit misleading, since they are always based on January-to-January. And we don’t only buy and sell in January. Sometimes we buy or sell in June or October.
A while back I posted a chart from J.P. Morgan showing the difference between calendar year returns and intra-year returns for the S&P 500.
The same obviously can happen with bonds.
There are a couple of different models we can use to generate monthly bond returns.
“The Simple Model”
This is how Damodaran and Ibbotson (among others) calculate bond returns. You buy a 10-year bond. The next year you sell the 10-year bond and buy another one. When calculating how much you get for selling your old bond, you pretend it is still has a 10-year maturity — that way you don’t need to muck around trying to figure out how much a 9-year bond might have been worth in July of 1923.
This model is straightforward & simple. You can do it pretty easily in a spreadsheet with a present value calculation using the new rate and the old rate.
=pv(current rate, 10 years, old rate, 1)
Then you need to add in any interest you received.
Here’s a spreadsheet that has imported Shiller’s most recent data (www.econ.yale.edu/~shiller/data/ie_data.xls) and performs these straightforward calculations.
Monthly Bond returns (calculations for simple model from Shiller data)
Calculations Stock Market Data Used in" Irrational Exuberance" Princeton University Press, 2000, 2005, 2015, updated…
Now we can take those numbers and try to compare them to something to see how we’re doing. The Bloomberg Barclays Intermediate Treasury Total Return USD sounds like exactly what we want. And Morningstar provides weekly & monthly data for it.
Here’s a spreadsheet that compares our “Simple Model” versus the Barclays Index.
Monthly Bond returns (Damodaran math)
Correlations Damodaran correlation, 0. 8899665402 Longinvest correlation, 0. 9253731101 Annual Comparison Year…
A telltale chart shows the ratio of cumulative returns. Ideally, we want this to be a straight line at 1: that means the two are an exact match. Whenever the line drops below 1, it means our cumulative returns are less than the index. When the line is above 1, it means our cumulative returns are greater than the index.
The “Simple Model” has resulted in us overstating returns by 0.71% a year. It has a correlation with the index of 0.8899655872, according to our spreadsheet.
Now let’s go back to our bond fund simulator. Previously it was just using annual rate data. But we also have monthly rate data available. With a few small tweaks we can use that monthly rate data to calculate the value of our fund every month, not just once a year.
What this means is that our bond fund:
- Has 7 bonds (a 10-year bond, a 9-year bond, etc, all the way down to a 4-year bond)
- The bonds pay interest every month; we keep that money in cash in the fund.
- Every January we sell the youngest bond. We buy a new 10-year bond using the proceeds of the sale and any interest we accumulated during the year.
On the surface, this sounds like an improvement. Though keeping all the interest in cash for a year doesn’t sound so great.
Here’s a spreadsheet of the results.
Monthly Bond returns (Bond Simulation 10-4, Annual Turnover)
Correlations Annual Turnover correlation, 0. 92537368 Longinvest correlation, 0. 92537368 Annual Comparison Year…
This look like an improvement. It still is far from a straight line but we shouldn’t expect perfection from a simple model.
We are still overstating the annual growth: the index grew at 6.96% and our model grew at 7.38%. So we’re overstating it by 0.41%. That’s less than the 0.71% of the Simple Model. And our correlation has gone from 0.88 to 0.92537368.
This model still has two things that don’t seem so great:
- We’re keeping cash around for a whole year, instead of reinvesting the interest as soon as we receive it.
- We only ever buy & sell bonds in January.
Now we’re going to stretch our simulation a bit. Instead of having one bond for each year, we want to have twelve bonds for each year. One for every month. That means for our multi-year ladder we won’t just have seven bonds any more. We’ll have over 70. And every single month we’ll sell a bond and replace it with a new one.
We won’t ever have any idle cash sitting around.
We’ll also be a bit more sensitive to changing interest rates, since we’ll be buying bonds every single month. Previously if the rates dropped in February but recovered in March it only showed up as a temporary blip in our price. But now we’ll be buying one of those low-rate February bonds and holding it for years, causing a constant, on-going impact on our returns.
Here’s the spreadsheet and telltale chart.
Monthly Bond returns (Bond Simulation 10-4, Monthly Turnover)
Correlations Monthly Turnover correlation, 0. 9307994284 Longinvest correlation, 0. 92537368 Annual Comparison Year…
This is a bit of a mixed bag. Now our average returns are 7.74% versus the index returns of 6.96%. That’s a difference of 0.77%. That’s worse than even the Simple Model. On the other hand, our correlation has improved going up to 0.9307994284.
Hmmm…not sure what to make of that, to be honest. I don’t like how much we end up overstating returns compared to the actual index. The correlation improvement is very marginal compared to the Annual Turnover model.
There’s clearly more digging that needs to be done. Though at some point we have to just throw up our hands and accept our model about the past is imperfect and live with that imperfection.
I think for my personal testing, I’ll stick with the monthly numbers generated by the Annual Turnover model for now.


Prisms and Pyramids
This Miniclip reviews the features of three-dimensional shapes and introduces prisms and pyramids. It explains polygons and polyhedrons, defines prisms and pyramids, and deconstructs a variety of examples including triangular prisms, rectangular prisms, hexagonal pyramids, triangular pyramids, and more. Students will learn how to connect these three-dimensional shapes with their nets, and how the net of a 3D shape can be constructed in various formations.
Production Year: 2020
Duration: 6 min
Printable Resources: Yes
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M.C Escher, Kaleidocycles 2nd Ed.
Intricate patterns and mind-boggling graphics are trademarks of the fascinating creations of M.C. Escher.
This set puts his magical visual world right at your fingertips with 17 easy-to-assemble paper sculptures, transforming his repeating patterns into three-dimensional polyhedra, while the book reviews the geometric principles and artistic invention underlying Escher’s optical marvels.
17 easy-to-assemble paper sculptures and book, 8.3 x 10.6 in., 64 pages, in a box, 10.2 x 12.7 x 1.6 in.


Rational relationships End behavior of rational functions: Mixed Multiplication Review – 5. Number and Operation Goal 1. Multiplication and division of whole numbers and fractions-concepts, skills and problem solving Expected Fluency: The digit is in the hundreds place.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Functions Determining whether a function is invertible: Addition Puzzles – 5. Y Understand More information. Adding and subtracting complex numbers: Vocabulary equivalent ratio rate ratio table Goals Students will understand that ratios with fractional terms can turn. Rounding Decimals – 5.
Convert tenths to hundredths as needed. The student adds, subtracts, multiplies, and divides to. Unit 6 Number and Operations in Base Ten: Lesson Dividing Rational c. Use the place value chart and metric measurement to compare decimals and answer comparison questions. Measurements can be seen in the form More information. Write your answer as a decimal.
Eureka Math Grade 5 Module 5 Lesson 6 | MathVillage
Use the place value chart to answer the following questions. Opposite Quantities Combine mafh Make Zero Refer to the integer game when answering the following questions. Shade the equivalent amount on the area model, drawing horizontal lines to make hundredths.
They are presented with. Complete the number sentences. The snowfall in Year 1 was 2.
Express your answer as a mixed number. Whole Number and Mixed Number Operations – 5. We have teachers that can easily cover a broad range of areas.
Plot the following points on the number line using decimal form.
Mafh a simple math drawing. Learn how to take two basic functions and combine them into a new function which is their sum, difference, product, or quotient. Oct 4, Homework Problem Solving English Learners.
Chart accurately labeled; 40; 40; disks. The 16 pages More information. The digit is in the hundreds place. After a lesson on exponents, What is different about the two answers?
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Algebra II | Khan Academy
A Story of Units: What time is it? Draw the new shape below. Fill in the blank to make the sentence true in both fraction and decimal form.
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The purposes of Biometrical Letters are:
- publishing papers dealing with various aspects of the analysis and interpretation of results from biometrical experiments, using mathematical and statistical methods;
- promoting and extending the use of statistical and mathematical methods in the principal disciplines of life sciences by reporting on the development and application of these methods;
- presenting statistical and mathematical tools useful in biometry. Methodological developments should be motivated by interesting problems from life sciences, applied or applicable;
- publishing review papers and papers presenting practical use of various methods of data analysis and statistical inference.


Numbers zero to five, Representing on fingers and other concrete counting, Counting stamps, claps and jumps to 10 and beyond where appropriate, Regular referral to calendar, weather, days of the week, months of the year, shape, pattern.
Recognising numbers 0—10, Representing on fingers and other concrete counting (show me), Counting 0-10 – Zero Superhero, Number formation (gross motor) with paint, with fingers in sand, with marbles running around number templates Identifying shapes in the environment Positional language, Shapes for different tasks (block building).
Moving on to showing numbers 0-10 on fingers. Link to familiar songs: Ten Little Monkeys Once I caught a fish alive. Counting stamps, claps and jumps to 5 Maths meetings – to include numbers to 10. Shape hunts.
Building confidence showing 0-10 on fingers, Identifying different shapes based on properties. Exploring measuring using unifix, Relative size: small, big, biggest. Reasoning with shapes.
Using marks to represent number (tallies) then representing with unifix cubes (simple bar modelling), Strategies for counting with 1-to-1 correspondence, Model using giant counting frame. Move and count and point and count strategies. Using shapes to make other shapes: Community Playthings blocks: triangular shapes can make a square or a rectangle.
Numberblocks (1-5) – link to NCETM materials Making numberbooks, Reinforcing counting using objects with 1- to-1 correspondence. Using marks to represent numbers. Comparing groups of objects: more, fewer, the same. Investigating capacity, weight, time.
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Babylonian and Greek Trigonometry: The Land that Impacts Mathematics
Certainly the very word ‘trigonometry’ might bring up a wince in you. Horrible memories from high school or college with sine, cosine, or secant charts. Or maybe you just avoided it because it just sounded terrible. If you heard of it at all.
Let’s make it really easy, though. Trigonometry simply means ‘measuring triangles’ and is a branch of mathematics that is interested in measuring movement and distances of things and angles and using triangles to make it work. If you have ever tried to move a table through a narrow doorway or figure out if you can stay walking at the same pace across a street and not get hit by a car traveling at a steady rate, you were doing trigonometry in your head. In the ancient world it was used for construction and charting astronomy.
Greeks did their math and counting in what is called ‘Base 10’ and it the same base we use in our counting system.
Babylonians did their math and counting in what is called ‘Base 60’. We have remnant of this sexagesimal system in our time keeping – 60 seconds in a minute, 60 minutes in an hour – and measuring angles with 360 degrees in a circle. Also base 60 is still part of longitude and latitude measurements. Hey, Babylonians also gave us zero. So, thanks Babylonia!
Base 60 is very flexible and has lots of benefits and…we don’t use it because our understanding of math came from the Greeks.
It happens to be that trigonometry the way the Greeks conceived of it, about 2500 years ago, absolutely works, but it is hard. Even for them. Base 10 isn’t really good for the math of trigonometry. Take my word for it. You might recall from a geometry class years ago using a protractor to measure angles. The Greek method of trigonometry requires measuring or predicting the internal angles of triangles usually when the triangle is placed inside a circle. It’s complicated.
Don’t worry too much about the particulars here…just go with me here! Greek trigonometry is hard because it works in base 10 and involves lots of interior angle measuring and predicting with triangles in a circle.
A Babylonian tablet, called Plimpton 322, which is about 4000 years old, much older than Greece or the Greeks even thinking about trigonometry, was recently translated from its cuneiform. And it was a trigonometric table done in base 60, so much more accurate, and much simpler but done in a completely different way even beyond base 60. The Babylonians used ratios based on the sides of squares and rectangles.
This tablet, found in the 1930’s was known to be a math table but they couldn’t figure out what it was talking about because all the people working on it only knew Greek style trigonometry. Daniel Mansfield from the University of New South Wales said of the tablet and the discovery
“This is a whole different way of looking at trigonometry. We prefer sines and cosines… but we have to really get outside our own culture to see from their perspective to be able to understand it.”
Now nobody truly knows why the better and easier method of trigonometry was forgotten for more than a thousand years and then a harder and worse one was invented.
But I have a pretty good guess why and it has everything to do with culture and how the land speaks through a culture.
The Babylonians lived in what is called ‘The Fertile Crescent,’ a big flat plain near the Tigris and Euphrates rivers. This area is one place where agriculture really started to be intensively practiced. In dividing up their land for parcels it was a bit like drawing on a huge flat and square piece of paper. The plots were all rectangular and regular sized. Some were bigger, of course, and some were smaller, but they were dependably rectangular.
The Greeks also had agriculture but their land was much more rocky, irregularly shaped, steep, and harder to till.
So here is my guess – The Babylonians created a trigonometry that relied on rectangles and the ratios of the sides because the land trained their eyes to see the world that way. Greeks created a trigonometry that relied on internal angles and triangles because the nature of their land made them look, and therefore see, in a more interior and less expansive fashion.
Now I don’t know that I am right or not but there is evidence that climate and altitude can impact the structure and sound of a language, so it isn’t out of the realm of possibility that terrain and geography could shape how a culture would devise more complicated math.
You might be wondering at this point…’this is maybe a little interesting’ or ‘where is he going with this?’
This piece isn’t to laud Babylonian trigonometry as being superior and Greek trigonometry but to have an example of when a culture is really in touch and relationship with their landscape that their work in the world will be an expression of their environment somehow and to understand how we proceed in the world as sometimes being hard and complicated it could have something to do with a challenging geography that we inhabit that impacts not only our eyes but the very capacity to see in a certain way.
My wish is that these stories and Primal Derma is a small part of retraining our eyes towards a different kind of landscape that will allow us to see outside of our usual story and biases like those mathematicians had to do to understand Plimpton 322.
Thanks for wondering about this.
Until soon enough,


Python is a programming language that lets you work more quickly and integrate your systems more effectively. You can learn to use Python and see almost immediate gains in productivity and lower...
python. Quaternion.py. """ Quaternion provides a class for manipulating quaternion objects.
Quaternion.Slerp. 想像するならば、物音に気付いてこちらを振り返る敵や、戦闘機がスピンするとき。 一瞬でこちらを向くのではなく、ゆっくりと連続的に向いてほしいときは、
J'ai Quaternion(axis, angle) constructor les Quaternion(axis, angle) constructor et Quaternion.slerp mais les deux résultats ont également été obtenus.(Quaternion.slerp a travaillé en utilisant une troisième valeur entre les deux) Mais vous pouvez utiliser la formule donnée sur ce wikipedia page:
Implementation of a quaternion q=a+bi+cj+dk. A quaternion is often noted q=(s,v) where s is a You can set a quaternion using various rotation representation with the help of the CRotation class.
DigitalRune Animation and the SrtTransform type uses LERP (linear interpolation) operations instead of a SLERP (spherical linear interpolation) operation to interpolate quaternions. Using LERP is faster, and the difference to SLERP is negligible in most cases.
The quaternion's rotation axis. pyrr.quaternion.slerp(quat1, quat2, t)¶. Spherically interpolates between quat1 and quat2 by t. The parameter t is clamped to the range [0, 1].
dot=Quaternion()|Quaternion.from_x_rotation(np.pi/2.0) class pyrr.objects.quaternion.Quaternion angle Returns the angle around the axis of rotation of this Quaternion as a ﬂoat. axis Returns the axis of rotation of this Quaternion as a Vector3. conjugate Returns the conjugate of this Quaternion. This is a Quaternion with the opposite rotation ...
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and indicates quaternion conjugation. Note the above quaternion multiplication results in a quaternion with the real part, , equal to 0. The , , and parts of the result form the rotated point (, , ). Consider the example of point rotation from above. The point (0.7, 0.5) was rotated 30 degrees around the Z-axis. Sep 04, 2010 · Python Rust Swift Qt XML Autres SGBD. SGBD & SQL 4D Access Big Data DB2 Firebird ... public Quaternion slerp (Quaternion q1, ...
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The quaternion can be defined by Eq. (5): Quaternion.slerp(q0, q1, amount=0.5) - class method. Find a valid quaternion rotation at a specified distance along the minor arc of a great circle passing through any two existing quaternion endpoints lying on the unit radius hypersphere. Source.
Mar 23, 2012 · So I have two variables: idealEuler and correctRotation both of type Vector3. correctRotation holds the value that idealEuler should have. idealEuler get's it's x and z parameters leaving the y different. This is feels consistent with using a half angle in the quaternion construction. (And using half of the translation in dual quaternion construction) Note that you will likely need to update any quaternion code that assumed that x 2 +y 2 +z 2 +w 2 = 1. This may include slerp, matrix conversions, point transformation and others.
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A quat represents a quaternion type that can be used to store rotations. A quaternion contains four values of which one can be seen as the angle and the other three as the axis of rotation.
Dec 19, 2018 · A new category of quaternion-based transformations are available in scipy.spatial.transform, including spherical linear interpolation of rotations (Slerp), conversions to and from quaternions, Euler angles, and general rotation and inversion capabilities (spatial.transform.Rotation), and uniform random sampling of 3D rotations (spatial.transform.Rotation.random). Quaternion.Slerp static function Slerp (from : Quaternion, to : Quaternion, t : float) : Quaternion Description. Slerp interpolates two Quats accurately and precisely which requires more power, Lerp...
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1.4.1. First-Person Shooters (FPS) http://en.wikipedia.org/wiki/First-person_shooter. 1.4.2. Platformers and Other Third-Person Games http://en.wikipedia.org ...
SLERP is very suitable for quaternion interpolation between only two orientations. Specifies the rotation interpolation mode for the curves after converting. Possible choices are "none" (unsynchronized Euler-angled curves which are compatible with pre-4.0 Maya curves), "euler" (Euler-angled curves with keyframes kept synchronized), "quaternion" (quaternion curves with keyframes kept synchronized, but the exact interpolation depends on individual tangents), "quaternionSlerp ...
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Quaternion.LookRotation Euler Lerp Slerp. Rigibody mass velocity useGravity isKinematic. AddForque ... Python零基础入门学习2020最新版（SiKi） 4594 29.
May 05, 2019 · A simpler way of averaging quaternions is possibly just to sequentially lerp or slerp between pairs of quaternions and adjust the weights at each step but this may or may not be accurate depending on the order in which you select the pairs. There's some debate on the best way to do this. Jan 31, 2016 · var lookDir = get_node(lookTarget).get_transform().origin - t.origin var rotTransform = t.looking_at(lookDir,Vector3(0,1,0)) var thisRotation = Quat(t.basis).slerp(rotTransform.basis,value) value += delta if value>1: value = 1 set_transform(Transform(thisRotation,t.origin))
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If you do e.g. Quaternion.Euler(55f, 0f, 0f) you get a completely different result than quaternion.euler(55f, 0f, 0f). Unity.Mathematics 0.0.12 preview 19 Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock.Compared to rotation matrices they are more compact, more numerically stable, and more efficient Ein ...
top. Modules and Header files. The Eigen library is divided in a Core module and several additional modules. Each module has a corresponding header file which has to be included in order to use the module. The faces are rotated using quaternions and spherical linear interpolation (SLERP), and the whole thing is rendered in OpenGL. The code for the cubies and cube is also on my GitHub.
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- Discovering examples
- Building compact discrete domains
- Introduction to input file
- Plugins and input files
- Initialize project
- Initialize your first custom plugin
- Implement your first custom plugin
- Run your first project
- granoo-viewer usage
- Inputs/Outputs with GranOO
- Building a very simple tensile test (You are here)
- Using numerical sensor
This page describes how to build a real simulation
You must follow the previous tutorial steps before starting this tutorial. You need results of previous tutorial steps. These results will be used as input data for this simulation. More precisely, you need this discrete domain
Please copy one of this domain in the current folder as it follows
Now, your current directory must look like
The input file
The goal of this simulation is to clamp the discrete element at the left and load the discrete element at
the right. This simulation can be set through input file only. You can create a new input file
tensile.inp with the following input.
Step by step description of input file
The following plugin loads a discrete domain file into the simulation
The following plugin converts all the
ElementPair (described in a previous tutorial step)
into mechanical beams.
To get full description of what this beam are, you can
consult the scientific bibliography.
The following plugin computes the optimal time step. It corresponds to the higher time step that ensures stable simulations.
The following plugin clears all the forces and torques applied to elements and bodies. After this plugin the domain is completely relaxed.
The following plugin applies a force on all the discrete elements indexed by the
left SetOf. Here, only
one discrete element is concerned. The
X=... corresponds to the value of the force along the X axis.
A mathematical formula is given that corresponds to : if the iteration is lower than 1,000, the force
is 100,000 times the iteration value or zero instead.
The following plugin computes the mechanical induced by the deformation of beams. The given loads are applied to the connected discrete elements.
The following plugin applies the velocity verlet integration scheme that computes linear and angular accelerations, velocities and displacements.
The following plugin imposes displacements to a discrete element set. Here the discrete elements are clamped (they can’t move).
The following plugin checks if the computation is right.
The following plugin saves the current state of the domain all 100 iterations.
Running example and showing results.
Run the example
Show the result
You should see the
granoo3-viewer window. If you press the Read button, you should
see an animation where you domain oscillates.


Welcome to the website of Professor Ibrahim Halloun.
This site provides research-based materials for educators at various grade levels, especially science and mathematics educators in grades 8 through 16. Materials include books, journal articles, and other sources published in English, French and/or Arabic, and pertaining to systemic cognition and education, and to modeling theory in science education. There also materials about educational policy, curriculum design and reform, and, especially, assessment and evaluation. The principal author of these materials is Prof. Ibrahim A. Halloun who is internationally renowned for his work on pedagogy and curriculum reform, and the tools he produced to ascertain learning, instruction, and science and mathematics curricula.


AHSC Junior Leadership Team - 6 Questions in 6 Minutes with Mr Vokes-Dudgeon
The Junior Leadership Team are back and putting another staff member in the hot seat.
This week, JLT Rep James K and JLT Treasurer Archie ask our Deputy Headteacher, Mr Vokes-Dudgeon, the questions everyone wants answered!
Archie - What is your favourite restaurant?
Mr Vokes - Dudgeon - I do like going out for dinner. It's one of my favourite things. I think my favourite restaurant that I think you'd like as well Archie is Nando's.
James K - What's your favourite time of the year?
Mr Vokes - Dudgeon - I think my favourite time of the year is summer because it's hot. And you get lots of sport being played and we have a lot of time off. We get the long summer holidays and it's just a good time to go away with your family and friends and enjoy yourself.
Archie - What's your favourite film?
Mr Vokes - Dudgeon - I think I'm going to go for the James Bond films. That's a bit of an easy answer because there are so many, if you want me to be specific I think it's Casino Royale.
James K - Whats your favourite meal of the day?
Mr Vokes-Dudgeon - I think it's dinner time at night because I like cooking and that's the time for me to go home and have a time cooking a meal. I might cook a curry, or fajitas, or chilli.
Archie - what was your favourite subject at school?
Mr Vokes-Dudgeon - So my favourite subject was maths when I was a student, I really enjoyed maths. I enjoyed trying to work out the problems and trying to get to the answer and I liked it when I could get the answer right. I could get that tick and I knew I'd got it right. And that's why I became a maths teacher.
James K - Whats your favourite favourite animal?
Mr Vokes-Dudgeon - I love animals. James. I think if I didn't work in a school, I'd like to work with animals. you know what what? I might go for a giraffe. I do like all the African animals that you see on Safari. I think going on safari would be amazing.
Thanks for letting us interview you Mr Vokes-Dudgeon!


Numbers are often problematic for both beginner and higher level learners, and students need regular and ample chance to practise them. Low numbers are generally brought into beginners courses quite early on, but even these create difficulties. They may have difficulty remembering the way three changes to thir- in thirteen and thirty, and similarly five to fif-. Or problems with pronunciation and stress patterns may lead to them confusing thirteen fourteen, thirty and forty. When high numbers are introduced, if they’re using British English, they’ll have problems remembering where to put the and : two thousand three hundred and twenty not two thousand and three hundred and twenty.
This activity aims to give students practice in pronouncing these numbers. You can adapt it to include only the numbers which the students have learnt up to that point, but I’ll describe it here using both low and very high numbers.
You need to make a series of cards with a number in figures (eg 10) on one side and in words (eg ten) on the other. The game can be played in pairs or in larger groups – six or seven is fine. The bigger the group the more cards you need on the table – aim for at at least ten per student.
The cards are laid out on the table number side up. In turn, each student chooses a card, says what s/he thinks will be on the other side, and then turns the card over. If s/he has said exactly what is written there, s/he keeps the card. If not, the card is turned back over and left on the table. The next student can’t choose the same card, but the student after that is free to do so if s/he wishes. At the end, the student with the most cards is the winner.
This seems simple, and with very low level students who are just learning the initial numbers it is best left like that. However, at a later stage it becomes more complex – what is written on the card is not always the exact number. For example, the student who sees 203 and says two hundred and three may turn the card over to find about two hundred. Some of the numbers will be exact, others approximations.
This has two advantages :
- Firstly, it extends the game. The student who says two hundred and three has had productive practice in pronouncing the exact number, but has also had receptive exposure to the approximation – which s/he or another student must later use. It may of course work the other way – the student who sees 4,999 and, thinking s/he has understood the trick, says about five thousand may turn the card over to find four thousand, nine hundred and ninety nine, or more or less five thousand.
- Secondly it helps the weaker students. Played the “straight” way, inevitably the weaker students make mistakes and have to turn the card back over while the stronger ones get it right first time. Introducing the element of chance means that, even if they have said something perfectly correct, the stronger students still may not win the card, and having already seen the correct version the weaker students have a better chance of being right when they pick it up.
A Variation : Telling the Time
The game can also be used to practise expressing the time. By far the simplest way of expressing the time is to use the hour/minutes system - It’s ten twenty five. This is the system which I teach immediately to beginners. However, by the late elementary level they also need to understand the ten past two/twenty to twelve system (or the American equivalent). Once this has been presented and practised in isolation, the game can be used to integrate the two.
In this version, the cards have a clock showing the time on one side, and the written time on the other. But for eg 9.20, the card may say either it’s nine twenty or it’s twenty past nine. Times like 10.24 may be expressed as its ten twenty four, it’s twenty four minutes past ten or as it’s almost ten twenty five, it’s about twenty five past ten etc. The amount of uncertainty makes it very unlikely that the cards will be guessed first time, and vastly increases the amount of both receptive exposure and productive practice which the students receive.
For both variations of the game there are more approximating expressions which could be used. For numbers -nearly, almost, just over, just under, around, around about, approximately, coming up for, a bit more/less than, and for times nearly, almost, just gone, around, approximately, coming up for etc. It goes without saying that the exact number of possibilities should be geared to the level and ability of the students : too simple and it’s boring, but too difficult and it’s demotivating. It’s up to the teacher to decide how many different expressions to include – perhaps none at all for complete beginners, but a lot if you want to use the game as a remedial activity at intermediate level.


The simple divide and conquer abstraction of MapReduce that we saw in the past lecture is immensely powerful for large scale data analysis. Many of the common statistics that we are interested in computing fall into this formulation.
For example, to find the maximum of a set of numbers, we can partition the dataset into multiple groups, find the maximum of each group and return the maximum of the group maxima. To find the average, we find the total sum associated with each group, as well as the number of elements in each, then combine these in an obvious manner. Not all functions can be computed this way—for example computing the median is much harder, as we cannot simply look at the median of each group. In fact, there is no deterministic algorithm that finds the median in one pass through the data without keeping all of the data in memory. Rather this requires a multi-pass approach, first finding the approximate range where the median lies, and then iterating through the data again to find the exact median.
While computing summary statistics is relatively easy once the data is in the right form, getting to this point usually requires a fair amount of work. For instance, we often have multiple input sources, each describing different aspects of the data—we may have one file describing the ratings that each person gave to each movie, a separate file with movie details (e.g., year of release, director, etc.), and yet another file containing user information (e.g., demographics, reported location, etc.). Thus if we want to find the movie from 1985 most watched by people in New York, we have to combine all of these datasets before issuing a simple maximum query.
This kind of combination is formally called a join. There are many possible kinds of joins—left, right, inner, outer, etc.—each of which performs the combination in a particular manner. For example, given a dataset mapping each user rating to a movie, and a movie to its year of release, an inner join on the movie name will produce a three column table—with a rating, movie name, and release year, but only for those movies that have both a rating and a release year; any incomplete rows in the resulting table will be dropped. On the other hand, a left join will keep all entries of the first table (here the movie ratings table) even for movies that have no release year, but will not produce movies with a release year but no ratings. Conversely, a right join will keep all entries of the second table, even for movies that have no ratings; finally, a full outer join will keep all entries and will fill in missing data whenever possible.
Typical analyses require multiple such joins followed by the relevant calculations on the resulting collections. While one can write a standalone map reduce program for each one of the steps, the logistics of managing the flow of these jobs and all of the intermediate data quickly becomes non-trivial. As we will discuss in coming lectures, Pig—a data processing language that is built on top of MapReduce—facilitates and simplifies the execution of these and other common MapReduce operations, including joins, filtering, sorting, and grouping.


BISECTING WITH A
If you have a compass (the mathematical drawing kind, not
the point-to-the-north kind), this is a simple three-part
PART ONE: Mark the legs
a) Open the compass to any distance (a “medium” one works
well) and tighten it so it stays that way.
b) Place the compass point on the angle’s vertex.
c) Using the compass’s pencil, make a mark on each leg of
PART TWO: Draw an
a) Place the compass point on the mark you made on one leg
of the angle, then draw a curve between the legs, in the
direction away from the vertex.
b) Do the same thing with the compass point on the other
mark you made. The two curves should intersect at a point.
PART THREE: Connect the
Using a straight edge, connect the angle’s vertex to the
intersection of the two curves you drew. Congratulations — you
just bisected the angle!


CCSD Recognizes Two Outstanding Educators with Superintendent's Game Changer Awards!
Superintendent of Schools Dr. Brian V. Hightower, right, Game Changer recipient Christy Cook, middle, and Oak Grove ES STEAM Academy Principal Penny Valle pose for picture after surprise presentation.
This week, Superintendent Dr. Brian V. Hightower recognized two extraordinary educators for their instructional excellence. Sequoyah HS mathematics teacher Julie Geoghagan and Oak Grove ES STEAM Academy exploratory lab teacher Christy Cook were presented with the Superintendent’s Game Changer Award!
Last year’s Game Changer awards were delayed due to the pandemic. Dr. Hightower awarded Oak Grove’s Christy Cook with the 2020-21 Game Changer Award for Instructional Excellence before a room full of her fellow teachers and coworkers during a staff appreciation breakfast on Tuesday. Ms. Cook was her school’s 2021 Teacher of the Year.
Dr. Hightower praised Ms. Cook for her work in helping to build the STEAM (STEM plus art) program at Oak Grove ES STEAM Academy.
“Oak Grove recently received its State STEAM certification after a three year process and a significant amount of dedicated work in the area of STEAM,” Dr. Hightower said. “Ms. Cook led the charge, and her hard work has paid off.”
Oak Grove ES STEAM Academy Principal Penny Valle credits Ms. Cook with leading the school’s initiatives to transform from a Fine Arts Academy to a STEAM Academy.
“She brought the STEAM to our school,” Principal Valle said. “Four years ago, Ms. Cook moved from a homeroom classroom to lead our STEAM lab. She effectively and enthusiastically developed and facilitated a lab that integrated Science, Technology, Engineering, Arts and Math and lead our faculty and school community in our STEAM journey.”
Dr. Hightower on Tuesday afternoon visited Sequoyah High School to surprise the 2021-22 Game Changer for Instructional Excellence winner, math teacher Julie Geoghagan, in a room filled with her peers.
“I was shocked, honored and humbled when the Superintendent recognized me for my continued efforts in striving to become a better teacher,” Ms. Geoghagan said of receiving the award. “I could not be the teacher I am without the support of the Sequoyah High School staff and the opportunities given by CCSD; I’m thankful to this district for continuously challenging me to be a better teacher!”
Dr. Hightower praised Ms. Geoghagan for being a “rock star math teacher” and engaging her students with mathematical reasoning by thinking outside the box to constantly improve and grow instruction.
Superintendent of Schools Dr. Brian V. Hightower congratulates 2020-21 Game Changer Award winner Christy Cook, while Oak Grove ES STEAM Academy Principal Penny Valle waits with open arms to congratulate Ms. Cook.
Superintendent of Schools Dr. Brian V. Hightower, left, poses with 2021-22 Game Changer Award winner Julie Geoghagan of Sequoyah HS, along with Sequoyah HS Principal Robert Van Alstyne.
Game Changer recipient Julie Geoghagan is congratulated by Superintendent Dr. Brian V. Hightower.


What is the most common unit of measurement of weight and mass? The simple answer is kilograms and pounds. The Pound is the imperial unit for weight or mass computation. Under the SI system, weight is the unit for mass and weight measurement. However, if you take an in-depth look inside both the terms, you will find complications. You might need to look at the different ways you will convert a measurement in both ways.
A kilogram is presented as “kg,” a pound is represented as “lbs.” The mother fact is that a kilogram is substantially heavier by 2.2 times than a pound. Thus, one can conclude that 1 kg= 2.2 lbs. To know more about the imperial and metric unit of measurement, keep reading the article.
The Basic Differences Between Pound And Kilogram
Did you know, the term kilogram is derived from a Greek word, whereas Pound is a German word? Kilogram, the metric unit of measurement, is used by several countries. However, the Pound is used by countries like the USA and UK. A pound is equivalent to 0.4535 kilograms. For example, if you want to convert 65 kgs to lbs, then the solution will be 143.3005 lbs.
How To Get The Answer:
The logic is simple: Divide the given kilos by 0.4535. We already know that a pound is equal to 0.4535 or 0.45359237. How many decimals places you wish to take depends on you. You are going to get the answer for converting 65kgs to lbs in no time.
Overall, the article has provided a brief guide about both the units of measurement. Keep in mind that the Pound is a measurement of force as well. Kilo is meant for mass measurement. While both the terms are utilized for computation but it has got significant differences.


Dr. Dana Randall is Co-Executive Director of the Institute for Data Engineering and Science, the ADVANCE Professor of Computing and an Adjunct Professor of Mathematics at the Georgia Institute of Technology. Randall received her A.B. in mathematics from Harvard and her Ph.D. in computer science from the University of California at Berkeley. Her research in randomized algorithms and stochastic processes bridges computer science, discrete mathematics and statistical physics.
She is a fellow of the American Mathematical Society (AMS) and a National Associate of the National Academies, as well as a former Sloan fellow and NSF Career award recipient. Dr. Randall has been the Program Chair for the SIAM Symposium on Discrete Algorithms in 2011 and the SIAM Conference on Discrete Mathematics in 2016 and was previously Director of the Algorithms and Randomness Center at Georgia Tech. She has served on the governing or advisory boards of the Institute for Mathematics and its Applications at the University of Minnesota, the Centre de Recherches Mathematiques at the University of Montreal, the Center for Discrete Mathematics and Theoretical Computer Science at Rutgers and the Center for the Science of Information at Purdue. Dr. Randall has received numerous awards for research, teaching and service at Georgia Tech.


Swix wc pro dh pole
Racing and freeride pole.
- Total weight 520 g
First-class racing rod in 7075 aluminum with downhill bend. Downhill grip and boot. Use:Racing, freeriding.
Multiply the body length by 0.7 to get the correct rod length. Round to the nearest whole number. For example:178 cm x 0.7=124.6 cm. 125 cm is the best rod length in this example.


This course is designed to introduce students to statistics and statistical methods. It is intended and designed for students who already have some familiarity with statistics. Students in this course will acquire the skills to create and comprehend statistical reports related to program evaluation and research practice. Students will be able to assess the value and limitations of measures of central tendency (means, medians and modes), rates, and statistical estimates such as correlations and regression parameters. This course will help students develop the ability to use advanced quantitative methods to describe and analyze real world situations in social work settings and to make ethical inferences and decisions based on the statistical results. Students will learn to choose methods of statistical analysis to improve social policy decisions, service delivery, and intervention programs. Students will learn to understand and use appropriate language with their statistical analyses to clarify meaning and to explain the inferences (e.g. causal inferences) that can be appropriately made from specific data.
1. Analyze extant research for its use and abuse of outcomes and measures of social justice, social change, and diversity.
2. Construct rates, means, proportions and other simple statistics and interpret them appropriately.
3. Ethically use and ethically report on the results of statistical analyses.
4. Identify appropriate simple statistical methods to use in policy and program evaluation situations.
6. Conduct basic statistical analyses of common policy and program evaluation situations.
7. Use basic descriptive statistics and test simple hypotheses to help answer policy or evaluation questions.
8. Construct meaningful and readable charts, tables, and graphs of appropriate data.
9. Prepare written, oral and visual reports for different audiences using simple and appropriate statistical language.
This course will use lectures, computer lab exercises, applied statistical exercises, case studies, and small group exercises to convey relevant content.
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Posts : 254 Points : 372 Join date : 2011-10-22 Age : 24 Location : Halmstad. Sweden
Subject: The Official Math Thread Sat Nov 12, 2011 5:32 pm
The Math Thread
So basicly, discuss math here. You can post questions and reply them with solutions if they're looking for some. Talk math in general, economy, whatever floats your boat. Peace and goodluck with the math everyone!


Train your brain with one of the most popular puzzle games of all time! In Sudoku, your goal is to fill a 9x9 grid with numbers so that each row, column and section contain all of the digits between 1 and 9. Can you master the logic challenge?
Just use your mouse. Move the cursor to the blank and select a number.
Most of the content in this gallery was produced by third party developers. GameSoft makes no representations about its performance, quality, or content.


Scholarships, Internships, and More
TAME supports careers in science, technology, engineering, and mathematics by offering scholarships to TAME club members who have been accepted into an accredited university or community college to pursue higher education in a STEM-related field.
Available scholarships vary year to year, but generally include:
The TAME Freshman Scholarship is awarded each year to a high school senior and TAME club member who has completed the Math and Science Competition and who will attend an accredited college or university to study a STEM subject. The scholarship amount varies based on available funding.
The TAME Evergreen Scholarship is offered to TAME scholars in their second to fourth year of study in a STEM field at an accredited college or university. The scholarship amount varies based on available funding.
The TAME TAMU Scholarship is a $2500 scholarship awarded each year to a high school senior and TAME club member who has completed the Math and Science Competition and who will attend Texas A&M University (TAMU) to study a STEM subject.
In addition, TAME partner universities occasionally offer scholarships to TAME students. Please contact TAME at (512) 471-6100 or at firstname.lastname@example.org for current opportunities.
In addition to our scholarships, we offer yearly employment opportunities for regional interns to work with TAME. Our regional interns are students at our partner universities. Working with the TAME state office and their regional chapter, they help to support and expand TAME programming and often serve as role models to current TAME club students. To find out more about becoming a TAME regional intern, please contact the TAME State Headquarters.


Lets be honest, math can be difficult for both students and parents. It’s one of the most difficult subjects students face in School. From personal experience, I struggled greatly. My parents even made me go to summer school to catch up on my mathematical struggles. Looking back, that extra time and school curriculum really did help. Unfortunately, this continues to be an issue we face in Washington State and the test scores reveal that there is a lot of room for improvement.
The Washington State Office of the Superintendent of Public Instruction released their recent test scores for both Math and English last Tuesday. While students did improve 3% from the previous year, it was unsatisfactory. The scores revealed that only 21.8% of Washington States 11th graders met the math standard. Washington State is considered to be in the bottom 3rd on a per pupil analysis. In addition, based on this data, that leaves 78% of our junior high school students below the overall standard. So what does this mean for our Seattle math students? It simply means that we have 1000’s of students who simply are not proficient enough in math and really need more help and/or better curriculum to get them to the next level.
What can we do to help our students with math?
- As a parent, we need to make sure to review our students activities as it relates to their homework and math scores. In short, be on top of their homework.
- Always be informed of your students math homework and be sure it’s being done on time.
- Follow-up on previous homework to evaluate your students results.
- If you notice that there is room for improvement, call the teacher and discuss what activities can be improved upon. If you’re student is misbehaving in class or not even going, you should be aware of this before asking. Teachers need to keep their students accountable as well. This includes informing you of their behavior.
- Hold your teachers accountable. It’s their job to discuss ways to improve your students math scores and how you can do better as a parent if you’re not helping the situation. Honesty is key so everyone needs to be transparent and accountable.
- If you feel your student is struggling in math, consider an outside teacher or additional tutor help. Schools have these resources available just call them and ask what department is appropriate and who you need to speak with.
- Consider outside curriculum to help you student. There are some great programs out there including the SWUN Math curriculum discussed below.
Washington State Math Curriculum Information & Help:
Our state uses the Mathematics and English Language Arts K–12 Learning Standards (www.corestandards.org)
One great program and resource is SWUN Math. For SWUN Math, it all started in a single urban classroom in California and is now educational movement focused on helping students with math. Founded in 2011 by Si Swun, many school districts across the country use them. They work with parents, teachers, and school administration to increase student scores and their involvement with mathematics. Their company focuses on the Common Core mathematics standards and they work side-by-side with school districts. According to their website, “The Swun Math Lesson Design carefully matches the eight required shifts in the Standards of Mathematical Practice, and inherently includes a gradual release of responsibility to students.” They provide coaching sessions to help principals and district staff learn their successful school-wide model. They also provide monthly reviews of the student assessment results as well as next step discussions based on those results. If you’re a parent not affiliated with a school district, you can find their math curriculum online such as Amazon.com as well as their iTunes App. Another resource they provide is their videos found on their official YouTube Channel. The company has put together math videos to help students learn more about math. They are always adding more videos and they are free to watch. This is a fabulous program that provides all the materials a school needs as well as ongoing support so students can enhance their math learning. The SWUN Math approach has been proven to help students with mathematics through clear learning, objectives, assessments, and goals. Twitter / Facebook.


Simple subtraction worksheets
Let’s help your child excel in math with our amazing free printable subtraction worksheets! Our worksheets are designed to not only teach the basic skills of subtraction but to also enhance your child’s writing abilities. Starting with simple pictures these worksheets are perfect for a smooth transition to number and picture subtraction. With our worksheets, basic number subtraction can be extensively practiced until it becomes effortless for your child.
If you are looking for an extra level of challenge, our math worksheet generator is at your disposal. You can customize the numbers, sums, and even generate solution sheets. You can make the worksheet as difficult or as easy as you choose. Watch as your child progresses through the levels of our worksheets and becomes a subtraction pro!
Picture subtraction problems: numbers 1-10
Free printable picture subtraction worksheets. Simple worksheets using pictures to teach kids to count and subtract.
Numbers and pictures with subtraction worksheets: numbers 1-10
Free printable subtracting pictures and numbers worksheets, this uses both math skills and writing skills.
Numbers subtraction worksheets: numbers 1-10
Free printable subtracting numbers worksheets.
Create your own subtraction worksheets
If you require something a little more challenging you can use our math’s worksheet generator to create your own maths worksheets. You have the option to select which numbers to include, the layout of the sums, how many sums you would like and finally the option to include a solution page.
Select the numbers. You can select a few individual numbers eg 1, 2, 3, 4, 5. Or you can select a range of numbers eg 1-10 or 1-20 etc.
Select the layout:
1 – 1 = 2
Select the number of problems:
Select whether you would like to print the solutions page:
Include solutions page
Click the button to generate your maths worksheet:
We understand the challenges that come with teaching subtraction to children and we believe that additional resources can be helpful in making it a more enjoyable and efficient experience for both you and your child. This website offers a wide range of materials, from worksheets to interactive activities, to make the learning process more engaging and effective. They also have tips and strategies on how to make subtraction fun and relevant for your child.


Guess who's been working on mathematical computations for the last two days for a customer?
a: The person with the best math skills in the office.
b: The programmers, because this client's requests spans unrelated segments of the database (or at least makes the report tool give silly numbers)
c: None of the above
d: The person with the inability to remember if you divide acres into money or money into acres to get the right answer (and cannot tell if the answer is right or not).
e: The person who works with the custom reports tool far too much.
f: The person who works to please the customer and gets criticized for "wasting" time giving the customer what they want.
g: Three consecutive answers above.
h: None of the above.
(Hopefully there will be an interesting post later today.)


Minitab is a statistical software mainly used for the analysis of data, which includes manipulating that data and identifying patterns and trends. It is written in FORTRAN and was developed by the Department of Statistics at the Pennsylvania State University. It was first designed to be a teaching package, designed for students in introductory statistics courses, making it more suited for instructional applications.
Minitab features a lot of tools to help in the analysis of data. It can employ basic statistics like descriptive statistics, normality tests, correlation, and outlier tests, but is also designed to do regression and analysis of variance. It can also create scatterplots, dotplots, charts, distribution plots, and rotating 3D plots. Multivariate analysis and forecasting are also possible in Minitab.Contratar a Minitab Experts
Hi, I am looking for someone who can develop a course on Minitab. The Minitab course outline is attached. The course topic will be "Using Minitab To Analyze Process Performance" If you are competent in Minitab and can create a course in Powerpoint (or provide the slides if you already have), please let me know with your price Thanks


Maths can be a tricky subject for many school children who struggle to understand the concept. This can lead to confusion, dislike and discouragement towards learning Maths.
However, math is not such a difficult subject – you only require a thorough understanding of the methods and practice. Children can achieve success by giving some more time and a little bit of understanding of Maths. One will achieve success and improve their skills in Maths in school.
Different Ways to Master in Maths in School
Learning in Class:
The classroom is the best place to learn Maths. Every child must remember that to improve math skills, one can start by paying attention to the class. Taking good notes or asking questions without any hesitation will help a child to understand Maths better. Also, create a study hour after school and revise the whole concept all over again to absorb it better.
As we know Maths is all about understanding concepts, practice and problem-solving at times. Do remember a child must memorize the concepts, not mugging up as it won’t be of much help. Learning one topic at a time and mastering upon it before going to the other one will be helpful for a child as all the concepts will be related to the previous ones.
Struggling with some methods? Get it cleared before going to the next topic. While learning math concepts, some children get stuck on some topics. If it happens sometimes, then do not skip it instead you can seek some help and get your doubts cleared. You can go to a teacher or friends to help you out in doubt clearing.
A Lot of Practice:
Practice a lot to get better in Maths and learn from the mistakes. One cannot understand the need for practice when it comes to the subject of math. The more you practice, the easier math becomes, a child must understand. You can also discover some shortcuts or techniques during this process. A child can check the speed and accuracy if they can give tests and quizzes.
These tips will help the school children become a master in Maths and get good scores to understand it better.


Well it has been long since I have come across the word Network. It seems to be a simple word with a general definition “an interconnected system of things or people”. But has ever anyone thought what would be the end line definition of this word. Well till date I have also not come across such a definition, which would limit the meaning of this word.
I have tried a lot to find the exact meaning of the word network but in vain because the domain expands to each and every thing we can imagine be it computers, humans etc.
Here what I am trying to deal is the computer networking concepts, their solutions and security that haunt us the most.
A general definition of the computer network could be “a computer network is a system for communication between computers” or “a data communications system that interconnects computer systems at various different sites”. Now the question lies in the point that how this data communication started or what was the base for this kind of communication to begin and so is the answer.
Theoretical Basis for Data Communication
Communication has been of prime importance in human life without which all of us cannot perform even our daily activities. As rightly said, “Necessity is the mother of all inventions” so was the idea that information can be transmitted on wires by varying some physical properties such as voltage or current. By representing the value of this voltage and current as a single valued function of time, f(t), we can model the behavior of signal and analyze it mathematically.
The Fourier Analysis provided the answer for the question and is said to be as base of networking concept.
It says “reasonably behaved periodic function, g(t), with period T can be constructed as a sum of a (possibly infinite) number sines and cosines”.
See the image for equation
So this was the starting of the communication over the electronic media. Here is a brief idea of relation between Fourier Analysis and Computers.
Fourier Analysis with Computers
There have been several techniques (tried and tested) that enable a computer to calculate the Frequency Spectrum of a signal. The first step in all cases is to convert the signal to a set of numbers for the computer to use. This is done by sampling the signal at a regular interval so that a table of values is created. Each sample value is separated from the next by a fixed period of time.
The number of points obtained and the time between samples combine to determine the length of time we look at the signal. Following definitions we take into consideration:
fs = sample rate in Hz
dT = 1/fs = interval between samples
N = number of samples taken
T = N x dT = total time period
f1 = 1/T = frequency of the first harmonic in Hz
For example, if we are interested in the AC power line and suppose we choose a sample rate (fs) of 6000 Hz and collect 100 samples (n=100). It gives the result as dT = 0.1167 msec and T = 16.667 msec. Then the first harmonic would be f1 = 60 Hz.
The traditional mathematical approach to Fourier analysis was based on approximating continuous waveforms but computer techniques can only deal with a set of samples. This does not change the basic idea of harmonic analysis but now we keep in mind the following:
1. The spectrums based on sampled waveforms can generate only N/2 harmonics.
2. If the original signal contains more than N/2 harmonics, the higher frequency harmonics will cause errors in the magnitude spectrum.
This type of error is referred to as Aliasing. Aliasing can be prevented by filtering the input signal before performing the Fourier analysis so that there are no frequency components above f1 and N/2.
The most popular computer algorithm for generating a frequency spectrum is the FFT or Fast Fourier Transform. As the name implies, the FFT is very efficient but it does have one quirk that affects the way it is used. The FFT can only process a sampled waveform where N (number of samples) is a power of 2. Acceptable values of N include 128, 256, 512 and 1024.
The FFT, like most computer algorithms, generates an Exponential Fourier Series, instead of a Trigonometric Fourier Series. The two series are identical except that the magnitude generated by the exponential series are half the value of the trigonometric series. Most application software automatically compensates for this and presents the magnitude spectrum as a Trigonometric series.


Q) How to calculate volume of a pipe in barrel if data is available in following units
Inner diameter in inches
Length in feet’s
Ans) Volume = Area × length
Area = 1/4× π × d²
Length = L
Volume = 1/4× π × d² × L
Volume = 1/4× π × (d²/144) × L ×(1/5.615) from in² to ft²
1 barrel = 5.615 ft³
Volume = (1/1029.4) × d²(in)× L (ft)
Q) Define Flow rate of fluid?
Ans) Flow rate of the fluid is the product of the velocity and are of cross section from where fluid is flowing
Q = AV m³/sec
Q) How you can create the jetting effect in fluid pumped at high flow rate?
Ans) Jetting effect can be produce in the fluid pumped at high flow rate by decreasing the area of cross section and this can be achieved by introducing the nozzle at the place where jetting effect is needed. Decrease in area will result in increase in velocity of fluid for keep the flow rate constant.
Q) What are five different units of density?
Ans) 1) Gram per centimeter cube g/cm³
2) Kilogram per meter cube kg/m³
3) Gram per litter g/l
4) Pound per cubic foot lb/ft³
5) Pound per gallon lb/gal
Q) What is difference between pump and motor?
Ans) Pump pressurizes the water by transferring its mechanical energy to the water and force it to move while motor uses the mechanical energy and pressure of flowing water to produce its rotation
Q) What is relationship between liter, gallon and barrel?
Ans) 1 barrel = 42 gallon
1 gallon = 3.78541 liter
So 1 barrel = 42 gallon = 158.98722 litter


The COVID-19 pandemic has brought with it many constraints on the teaching of mathematics. Particularly, educators had to switch instantly to online platforms when they had little or no experience of online teaching. Educators were faced with a situation where they needed to relearn ways of teaching mathematics within the constraints imposed by the pandemic. Inspite of the difficulties, this gave rise to innovative ways of teaching mathematics, and provided an opportunity for teachers and students to find new ways of interacting and working together.
The aim of this study is to explore how mathematics lecturers at MCAST embraced this change in teaching, with all its challenges, struggles and opportunites. What type of pedagogy was being used in mathematics education during the COVID-19 pandemic? Khirwadkar et al (2020) observe that switching to online teaching did not involve simply adapting face-to-face pedagogical strategies to a prescribed curriculum, but rather finding other pedagogical strategies while understanding that ‘what is not forbidden is allowed’; this in turn ‘opens a space of opportunities for reimagining mathematics education’ (p.45).
However, this study will also explore the vision of mathematics lecturers for the post-COVID-19 period. What pedagogical lessons were learnt from the experience of teaching during the pandemic? Will these experiences enrich their future mathematics teaching? In their research on online mathematics teaching during the pandemic, Ní Fhloinn and Fitzmaurice (2021) conclude that lecturers ‘have amassed experience, knowledge and resources that will complement their face-to-face teaching moving forward’ (p.15).
Hence, this current study will not only seek to “understand the emerging educational realities in the context of the COVID-19 pandemic”, but will also explore the way forward in mathematics teaching at MCAST (Khirwadkar et al, 2020,p.45). Focus will be on the teaching of Mathematics Key Skills at MCAST, and data will be collected by means of semi-structured interviews with a sample of mathematics lecturers. This will be followed by qualitative thematic analysis.
Ní Fhloinn, E. & Fitzmaurice, O. (2021). ‘Challenges and Opportunities: Experiences of Mathematics Lecturers Engaged in Emergency Remote Teaching during the COVID-19 Pandemic’, Mathematics, 9 (18), pp. 2303.
Khirwadkar, A., Khan, S.I., Mgombelo, J., Snezana, O-R., & Forbes, W.A. (2020). ‘Reimagining Mathematics Education During the Covid-19 Pandemic’. A Journal of Educational Research and Practice, 29 (2), pp.42-46.


RT @TeachersFed: At the crux of many issues assailing our system is the underfunding of our public schools, stuck at only 90% of the minimu…
RT @dizdarm: The Deputy Premier @pruecar & partners in public education signing a Statement of Intent to work together to lift the standing…
News & Events
Australian Curriculum for Mathematics: Overdue Reform or Same Old Same Old
August 3, 2021
Curriculum reform is always front-page news when it comes to a traditional disciplinary area such as mathematics. While it might seem that the subject matter of mathematics is universal, highly procedural, and unquestionable in structure and rigour, changes to what and how mathematics is taught have been happening in many countries for some time now. This opinion piece has been written by Dr Phil Lambert, Adjunct Professor, University of Sydney and Ellen Koshland, Founder, Australian Learning Lecture.
Read more: Australian Curriculum for Mathematics op ed


Susan Clark has taught computer classes to elementary, middle and high school students at Atlantis Academy Miami since 2006. Her students learn how to use popular Microsoft Office computer software, including Word, Excel, Publisher and PowerPoint, as well as the more complex Adobe Photoshop program. Before joining Atlantis Academy, Susan taught math at the Peace Corps in Africa and continued teaching computers and robotics as a Peace Corps fellow at Temple University in Philadelphia. Susan graduated from Florida Southern College in Lakeland, Fla., with a bachelor’s degree in computers and math. She holds a Florida teaching certificate in math (grades 6-12) and assists students weekly with their Ascend math curriculum in the computer lab.