- Monitoring of Offshore Wind Turbines Using Measured Accelerations and Hidden Markov Models with Physics-Based Initialization, IMAC-XL, Society for Experimental Mechanics, Feb. 7, 2022. This talk has been accepted for an upcoming conference
- Inference and imputation for hidden Markov models with hybrid state outputs, 2021.
- When Machines Learn, Method for Imputation with Hidden Markov Models [blog post], Oct. 30, 2020, https://medium.com/utility-machine-learning/methods-for-imputation-with-hidden-markov-models-be2900cfc2d2.
- When Machines Learn, Imputation and its Applications [blog post], Sep. 25, 2020, https://medium.com/utility-machine-learning/imputation-and-its-applications-86edc8ffa82a.
- When Machines Learn, Using Hidden Markov Models to Detect Seasonality in Sequential Data [blog post], June. 19, 2020, https://medium.com/utility-machine-learning/using-hidden-markov-modeling-to-detect-seasonality-in-sequential-data-3c059649eb70.
- Spinor Regular Ternary Quadratic Lattices, Institute for Computational and Experimental Research in Mathematics, April 18 (ICERM archive video)
- Almost Universal Ternary Sums of Polygonal Numbers, Southern Illinois University Carbondale, November 2017 (YouTube video).
- (with M. Dutour Sikiríc, J. Voight and W. van Woerden) A canonical form for positive definite matrices, Proceedings of the Fourteenth Algorithmic Number Theory Symposium, ANTS-XIV, Mathematical Sciences Publishers, 2020 (final version at arXiv:2004.14022).
- (with A. G. Earnest) Classification of one-class spinor genera for quaternary quadratic forms,Act Arith. 91 3 (2019) 259-287, (final version at arXiv:1803.03028).
- (with B. Kane) An algebraic and analytic approach to spinor exceptional behavior in translated lattices, Automorphic Forms and Related Topics, Contemp. Math., 732, 2019, Amer. Math.
Soc., Providence, RI, (final version pdf available here).
- (with A. G. Earnest) Completeness of the list of spinor regular ternary quadratic forms, Mathematika, 65 (2019), 213-235, (final version at arXiv:1711.05811).
- (with B. Kane) Almost universal ternary sums of polygonal numbers, Res. number theory (2018) 4: 4. https://doi.org/10.1007/s40993-018-0098-x Updated: January 19, 2021.
- (with A. Feaver, J. Liu, G. Nebe) On Kneser-Hecke operators for codes over finite chain rings, Directions in Number Theory: Proceedings of the 2014 WIN3 Workshop, Association for Women in Mathematics Series, Springer-Verlag,
- A characterization of almost universal ternary inhomogeneous quadratic polynomials with conductor 2, J. Number Theory, 156 (2015), 247-262.
- A characterization of almost universal ternary quadratic polynomials with odd
prime power conductor, J. Number Theory, 141 (2014), 202-213.
- (with W. K. Chan) Almost universal ternary sums of squares and triangular numbers, Quadratic and Higher Degree Forms, Developments in Mathematics, Springer-Verlag, (2013).
- (with K. Doerksen) Primitive prime divisors in zero orbits of polynomials, INTEGERS: The Online Journal of Combinatorial Number Theory, 12 (2012)


I get very annoyed by some very simple things.
One is when people cannot read simple numbers, especially examples like this:
How do you say this number?
Twenty five point six nine
You may want to put a hyphen in, but that’s got nothing to do with saying it.
It is not:
Twenty five point sixty nine
How would you say this: 38.1234? Thirty eight point twelve thirty four? This is nonsense.
Adding “..ty” to something refers to the tens column in a number, so eighty means eight sets of tens. After the decimal point, we have tenths, not tens.
It also annoys me that people cannot write simple numbers. On a game show a couple of days ago, some big celebrity I had never heard of wrote, in answer to a question:
If you can’t read it, there’s a comma in there. This is not a real number, unless you live on the continent and then it is one hundred point zero zero. The number intended was one hundred thousand. You would imagine that grown up adult human beings could write down a simple number, wouldn’t you?
I also find it sad that we use a full stop (.) to substitute for a decimal point (·). This is just laziness on the part of computer programmers, and is just plain wrong.


Japanese Technology Management Masters Program Entrance Examination Information
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Application Period：July 2, 2019 – July 11, 2019
Examination Schedules：August 26, 2019 – August 30, 2019
< Previous Tests of Mathematical Problems Designed to Test Ability to Think Logically>
Parts of the problems of “Mathematical Problems Designed to Test Ability to Think Logically” are the same problems as the mathematics problems of “Regular education subjects” of the School of Engineering. An examinee will be instructed to choose 2 out of 6 problems in “Regular education subjects” of School of Engineering, and 4 out of 6 original problems.
The past mathematics problems of “Regular education subjects” of the School of Engineering are available on the following webpage.
The past original problems are the same as those provided by the Department of Systems Innovation, which are available on the following webpage:
< Previous Tests of Reading Comprehension >
If you wish to receive a previous test, follow the following steps:
- Contact the administrative office of the Department of Technology Management for Innovation (see below).
- Mail a pre-addressed envelope (big enough that fits A4 size papers) to administrative office (see the address below).
The Administrative Office
Department of Technology Management for Innovation
Graduate School of Engineering, University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656 Japan


51 numbers are chosen at random from the counting numbers 1, 2, …, 100. Will those 51 numbers always contain a “consecutive pair”? That is, will there always be an N so that N and N+1 are in among your 51 numbers?
There are a number of reasons that I like this problem, but the main one is the surprising result that’s proven in the process of solving the problem.
We’ll use the Pigeonhole Principle, which is a common sense result that can be summarized as follows: If you have more objects than places to put them, when all of the objects are “put away”, at least one of the places must contain at least two objects.
To model the problem, imagine that you have 100 ping pong balls 50 small boxes (large enough to hold 2 ping pong balls). The ping pong balls are individually labeled with the natural numbers from 1 to 100, then placed in a large container and the boxes are labeled in pairs: the first box is labeled [1 2], the second box is labeled [3 4], and so on (officially, box K is labeled [2K-1 2K]). Notice that each ball will have exactly one box whose label includes the number on the ball.
Now, pick 51 balls from the container (therefore choosing 51 numbers from 1 to 100). Taking each of the 51 balls one at a time, place them in the box whose label includes the number of the ball. Since there are 51 balls and only 50 boxes, at least one of the boxes must contain more than one ball, which mean at least one of the boxes has to contain both balls whose numbers match the the label on the box. That is, at at least one pair of the balls are labeled with consecutive numbers, which solves the problem. Namely,
If 51 numbers are chosen at random from the natural numbers 1, 2, … , 100, then there will always be a consecutive pair of numbers among the 51 chosen numbers.
Interesting result, right? Well, wait, because there’s a lot more to this than might first appear. In fact, what we proved was that there will always be a consecutive pair chosen for which the smaller of the two numbers is ODD.
Now, that on its own might not seem so out of the ordinary, since you might expect that, since there are the same number of odds and evens from 1 to 100, there must also be a consecutive pair (among the 51 chosen numbers) in which the smaller of the two numbers is EVEN. Shouldn’t there be some sort of symmetry to this problem so that anything true of odd numbers must also be true for evens? However, this is NOT guaranteed – in fact there are many examples of 51 numbers (from 1 to 100) among which there are no consecutive pairs that “start” with an even number. For example, the 51 chosen numbers COULD BE 1, all the even numbers, for which the only consecutive pair is 1 and 2.
So, there will ALWAYS be a pair of consecutive numbers in which the smaller is odd, but there MIGHT NOT be a pair of consecutive numbers in which the smaller of the numbers is even. Why is our intuition that evens and odds should somehow be “the same” so wrong in this case?
Well, in a nutshell, it’s fairly easy to see what the big difference is: In the numbers from 1 to 100, there are 50 consecutive pairs in which the smaller of the pair is odd (1 and 2, 3 and 4, 5 and 6, … , 99 and 100), while there are only 49 consecutive pairs in which the smaller of the two numbers is even (2 and 3, 4 and 5, … , 98 and 99), so it’s more likely to pick an “odd starting consecutive pair” than to pick an “even starting consecutive pair”.
In terms of the method of our proof, if we instead forced our pairs to start with an even number, our boxes would be labeled [2 3], [4 5], [6 7], … , [98 99], but this collection of boxes has a significant problem: two of the numbers (1 and 100) are missing, so we need another box, which we’ll have to label [1 100]. Now, when our 51 numbers are chosen, at least one of them must have 2 ping pong balls in it. However, this box MIGHT BE the one labeled [1 100], so there might not be a consecutive pair “starting” with an even number.


Lecture Series: Models of Time and Probability | Hannes Leitgeb: Mathematical Philosophy: Past, Present, Future
The lecture series are part of the Thematic Einstein Forum “Scales of Temporality: Modeling Time and Predictability in the Literary and the Mathematical Sciences”. The forum is organised within the framework of the Berlin Mathematics Research Center MATH+ in collaboration with EXC 2020 “Temporal Communities” and supported by the Einstein Foundation Berlin.
The collaborative Thematic Einstein Forum Scales of Temporality: Modeling Time and Predictability in the Literary and the Mathematical Sciences aims to explore shared interests, common grounds and similar problems both the mathematical sciences and the Humanities, particularly the philologies and the literary studies, entail.
In the lecture series “Models of Time and Probability”, experts from mathematics (dynamical systems, analysis, probability theory, applications and modelling, biomathematics) and from literary studies (narratology, rhetoric, literary history and philosophy) will give lectures to an open audience.
Hannes Leitgeb (Ludwig-Maximilians-Universität München, Munich Center for Mathematical Philosophy) on "Mathematical Philosophy: Past, Present, Future":
"Mathematical/formal philosophy“ refers to the application of logical and mathematical methods to philosophical problems and questions. In recent decades, this mathematical way of doing philosophy has become a great success story. The talk will explain why this is so, how mathematics can be applied in philosophy, and what the future of mathematical philosophy might be like. Some of the examples in the talk will relate to the “models of time and probability“ theme of the lecture series.
26.01.23 | Xue-Mei Li (Imperial College London): Noise and Scales
2.02.23 | Paul Hager (HU Berlin): Time Scales in Rough Volatility
More information about the lecture series can also be found on the MATH+ website. The lectures start at 6:00 pm. Participation is possible both in person and online.
Time & Location
Jan 19, 2023 | 06:00 PM
Zuse Institute Berlin (ZIB)
For online link register by email to firstname.lastname@example.org.


Okay, I know it’s the weekend, and you’re probably still half-asleep and in no mood for math. But relax, this is fun math. Well, fun if you’re really into applied graph theory. There are pretty graphs to look at, and I promise you won’t have to solve any of those weird equations with all the funny symbols that make it look like your cat randomly walked across the keyboard. Oh, and it involves Game of Thrones. Maybe I should have led with that. Okay, we’ll start again: who is the most important character in Game of Thrones? Hint: it’s not Jon Snow. Sorry, fans of the bastard of Winterfell.
Mathematicians at Macalester College utilized network science, “a new and evolving branch of applied graph theory that brings together traditions from many disciplines, including sociology, economics, physics, computer science, and mathematics” to perform a network analysis of the HBO fantasy series. Andrew J. Beveridge and undergraduate Jie Shan examined A Storm of Swords, the third book in George R.R Martin’s A Song of Ice and Fire saga, and the basis of seasons 3 and 4 of the show. Their study revealed that three characters – Sansa Stark, Tyrion Lannister, and Jon Snow – are mentioned more than anyone else, but only one can be considered the book’s protagonist. “In our network, three characters stand out consistently: Tyrion, Jon, and Sansa. Acting as the Hand of the King, Tyrion is thrust into the center of the political machinations of the capitol city. Our analysis suggests that he is the true protagonist of the book.” The study does mention things like Eigenvector Centrality, combinatorial probability, and “a fast approximation algorithm called the Louvain method.” Well, of course they would use the Louvain method. I mean, what else would they use?


If you’ve ever found yourself standing in the kitchen, trying to convert fluid measurements, you may have asked yourself, “How many ounces are there in a gallon?” Well, wonder no more! In this comprehensive guide, we will delve into the world of fluid measurements and explore the conversion between ounces and gallons. Whether you’re a cooking enthusiast, a DIYer, or just curious about the intricacies of measurement, this article will provide you with all the answers you need.
Understanding Fluid Measurements:
Before we dive into the specific conversion, let’s take a moment to understand the basic units of fluid measurements. In the United States, the most commonly used units are ounces (oz) and gallons (gal).
- Ounces (oz): An ounce is a unit of volume measurement commonly used for smaller quantities of liquid. It is abbreviated as “oz” and is equivalent to approximately 29.57 milliliters or 1/128th of a gallon.
- Gallons (gal): A gallon is a larger unit of volume measurement typically used for larger quantities of liquid. It is abbreviated as “gal” and is equivalent to approximately 3.785 liters or 128 fluid ounces.
Now that we have a general understanding of these units, let’s proceed to the conversion between ounces and gallons.
Conversion: Ounces to Gallons
To convert ounces to gallons, we need to understand the conversion factor between the two units. As mentioned earlier, there are 128 fluid ounces in a gallon. This conversion factor allows us to easily convert between the two measurements.
Here’s the formula for converting ounces to gallons:
Number of Gallons = Number of Ounces / 128
For example, if you have 256 fluid ounces, the calculation would be as follows:
Number of Gallons = 256 / 128 = 2 gallons
Similarly, if you have 64 fluid ounces, the calculation would be:
Number of Gallons = 64 / 128 = 0.5 gallons
Keep in mind that when converting ounces to gallons, it’s important to divide the number of ounces by 128 to obtain the equivalent value in gallons.
Conversion: Gallons to Ounces
On the flip side, if you want to convert gallons to ounces, you can use the following formula:
Total Ounces = Total Gallons * 128
For instance, if you have 3.5 gallons, the calculation would be:
Number of Ounces = 3.5 * 128 = 448 ounces
And if you have 0.25 gallons, the calculation would be:
Number of Ounces = 0.25 * 128 = 32 ounces
Remember to multiply the number of gallons by 128 to obtain the corresponding value in ounces.
Understanding the conversion between ounces and gallons can be highly beneficial in various everyday situations. Let’s explore a few practical applications:
- Cooking and Baking: Recipes often call for specific measurements, and being able to convert between ounces and gallons will help you accurately follow the instructions. Whether it’s measuring liquids, such as water or milk, or ingredients like oil or syrup, knowing the conversion will ensure your culinary creations turn out just right.
- DIY Projects: Whether you’re painting a room, staining furniture, or mixing chemicals for a science experiment, understanding fluid measurements is crucial. Conversion between ounces and gallons will help you determine the appropriate quantities of paint, stain, or other liquids needed for your projects.
- Hydration and Fitness: If you’re tracking your daily water intake, knowing the conversion between ounces and gallons can be useful. Drinking an adequate amount of water is essential for maintaining good health and hydration levels. Having the ability to convert your water intake from ounces to gallons will help you track and achieve your hydration goals more effectively.
Now that you have a comprehensive understanding of the conversion between ounces and gallons, you’ll never be left guessing again. Whether you’re measuring ingredients for a recipe, tackling a DIY project, or monitoring your hydration, knowing how many ounces are in a gallon empowers you to make accurate calculations. So go ahead, confidently measure and convert between these fluid measurements, and unlock a world of precise measurements in your daily life!
Remember, understanding measurement conversions is not only practical but also empowers you to be a more informed and efficient individual. So, the next time you find yourself pondering the question, “How many ounces in a gallon?” You’ll be prepared with the information you need to easily traverse the fluid measurement world.


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My son, attending a private school during his freshman year, struggled with his math class. We set up tutoring for him with Phil Eagle. He was very professional. I think my son would have been lost without Phil. The services were provided in his home. We were welcomed to sit and wait for our student in their living room in full view of the tutoring room. You could hear the session going on. My son succeeded in his class. I would highly recommend Phil Eagle! -- Cynthia N.
prepared, began and ended on time. Appointments were always kept. They were very quick and accommodating to reschedule if we needed
I would again use, and, highly recommend Phil Eagle for math tutoring at any level. Two friends, as I had, also found him helpful and professional! -- Rosario V.
My high school sophomore son was failing his Algebra math class. Mr. Eagle helped him bring his grade up to a B+! Mr. Eagle, is a retired math teacher, an Air Force veteran, and, is good with kids. My son responded so well to him that not only the math grades came up, but, he also became more
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My older daughter needed only one math class - CBC 147 "Finite Math" - to receive her Junior College degree. She had taken it four times and failed it each time before she decided to get help. Math Tutor Phil was highly recommended and she began his individualized 1-to-1 tutoring. In just a few months she was not only able to understand the math concepts but was able to retake her math class a fifth time - and passed! Imagine the joy I felt as her father when she broke down in tears as she told me she had finally overcome the challenges which had prevented her academic success! -- Clint McB.
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Do you find mathematics to be a hard subject? Do you feel that mathematics is not your cup of tea? Then why don’t you engage yourself in some basic math games and make the learning process easier and fun, but where to find math games? Your search will end here.
Check out the list of some of the most popular websites which will help you to get engaged in fun mathematic activities.
Games are always fun. But when it comes to mathematics every joy seemed to have been drained of your life. This is not the actual case. In the current scenario with the help of different maths games and online math tutorials you can now easily enjoy this subject and make fun calculations.
Math Millionaire: In this game, you will get the option of choosing from different topic choices, including place value, an order of operations, algebraic expressions, and square roots. Then check how far can you make progress with the game so that you can understand the effectiveness of your calculation skills.
Basket ball math: This game includes an “adding decimals” option for younger children, and “2-step equations” for older students. Tying math into their interests can help turn it from work to play. So depending on your age, you will be able to play this game.
Soccer maths: Give your soccer-lovers a fun way to practice reducing fractions to their simplest form. Also, try rounding decimals, dividing fractions, or adding two-digit numbers. These are easy and fun.
Geometry games: engaging in this game will help you to learn the geometric calculations and figures from the very beginning. Challenge yourself to identify the different 3-dimensional figures in geometry. Play with the number and make the figures valuable. Then you will be able to access the calculations. Geometry doesn’t have to be hard! Prepare yourself for the basics by trying out different geometry games covering a range of topics.
Math Jeopardy: This tool will also help you to develop your maths skills by helping you play and identify from among the 2-dimensional figures and different calculations. This is majorly designed for the adult learners and will also involve some tricky game plays that will help you to improve your already present maths skills. So go ahead and develop your maths skills and make your friends feel less intelligent. And the fun part is now you can do that with only playing games. So games and maths will undoubtedly prove to be a great combination.
Coolmath games.com: it is a great site for the entire maths lover and also a great site for all those who do not love maths. Play games on this site and learn the basics of numerical calculations easily. The game topics in this site include fractions, money, algebra and place value. Unlike other sites, this site will help you with a high degree of maths basics and formulas that will be helpful for learning the basics.
Games.com: this is also a common platform for the maths games lover. This platform will allow you to get engaged in different numerical games and problem-solving cases. This site contains games majorly designed for the children within the age range of 4 years. These games will help the children in learning counting and additions and subtraction parts which will make them learn the basics.
However, it is not an easy task to start playing any maths games all of a sudden. You first need to plan it out in your mind. First, decide which version you’re going to play. Select the version of the game that you think is suitable for you. Then start playing. If you select the wrong version, then you may miss out some of the attractive parts of the games.
In short, there are lots of fun ways to encourage yourself in studying maths. These are especially helpful for those who find math boring or really challenging. Use the suggestions above and have fun with the maths games. If you are not a kid and still don’t like maths then also engaging in the maths games will make you fall in love with the subject. Try it out may be you will also become a maths lover.


Specifies the principle of the relationship between dimensional tolerances and geometrical tolerances. It shall be applied to linear dimensions and their tolerances, angular dimensions and their tolerances and geometrical tolerances which define the following four aspects for each feature of the part: size form, orientation, and location. Refers to ISO 286/1, ISO 1101, and ISO 2692.
Текущий статус : WithdrawnДата публикации : 1985-12
Версия : 1
Технический комитет:Dimensional and geometrical product specifications and verification


1 edition of Avery"s Plane geometry. found in the catalog.
Avery"s Plane geometry.
Royal A. Avery
|Contributions||Stone, W. C.|
|LC Classifications||QA455 .A96 1964|
|The Physical Object|
|Pagination||ix, 502 p.|
|Number of Pages||502|
|LC Control Number||64001179|
Two distinct lines perpendicular to the same plane must be parallel to each other. For example, a Averys Plane geometry. book straight line has no width, but any real drawn line will. A "line" in Euclid could be either straight or curved, and he used the more specific term "straight line" when necessary. There are two reservations. Pythagorean theorem[ edit ] The celebrated Pythagorean theorem book I, proposition 47 states that in any right triangle, the area of the square whose side is the hypotenuse the side opposite the right angle is equal to the sum of the areas of the squares whose sides are the two legs the two sides that meet at a right angle. In this post the Problems in Solid Geometry is taken up.
Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost. It is therefore possible to confine myself here to those points Averys Plane geometry. book this book differs from the first. Other figures, such as lines, triangles, or circles, are named by listing a sufficient number of points to pick them out unambiguously from the relevant figure, e. Because this geometrical interpretation of multiplication was limited to three dimensions, there was no direct way of interpreting the product of four or more numbers, and Euclid avoided such products, although they are implied, for example in the proof of book IX, proposition
A typical result is the ratio between the volume of a cone and a cylinder with the same height and base. Three parallel planes. The number of rays in between the two original rays is infinite. The next post would be Problems in Plane Geometry.
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The plane determined by Averys Plane geometry. book point P0 and the vector n consists of those points P, with position vector r, such that the vector drawn from P0 to P is perpendicular to n. The angle scale is absolute, and Euclid uses the right angle as his basic unit, so that, for example, a degree angle would be referred to as half of a right angle.
They aspired Averys Plane geometry. book create a system of absolutely certain propositions, and to them it seemed as if the parallel line postulate required proof from simpler statements. Flipping it over is allowed. The solutions, much like the book itself, are thorough and easy to follow.
Jack Chen jackchen5 hotmail. If equals are added to equals, then the wholes are equal Addition property of equality. All credits to the original uploader. The number of rays in between the two original rays is infinite. This prevents the necessity of interrupting the logical train of thought by turning to a previous section, and compels the learner to become familiar with a large number of geometrical truths by constantly seeing and repeating them.
Specifying two sides and an adjacent angle SSAhowever, can yield two distinct possible triangles unless the angle specified is a right angle.
His current mathematical interests are in modular arithmetic and cryptography. Main article: Euclid's Elements The Elements is mainly a systematization of earlier knowledge of geometry. Thales' theorem states that if AC is a diameter, then the angle at B is a right angle.
For example, a rectangle with a width of 3 and a length of 4 has an area that represents the product, In this text the student's attention is directed repeatedly to the relations of solid geometry to other school subjects, such as algebra, trigonometry, geography, and physics.
Triangles with three equal angles AAA are similar, but not necessarily Averys Plane geometry. book. Its improvement over earlier treatments was rapidly recognized, with the result that there was little interest in preserving the earlier ones, and they are now nearly all lost.
Some modern treatments add a sixth postulate, the rigidity of the triangle, which can be used as an alternative to superposition. A line and a point not on that line.
The subject of limits is exceedingly interesting in itself, and it was Averys Plane geometry. book best to include in the theory of limits in the second Book every principle required for Plane and Solid Geometry. For more information about the German court case, and the reason for blocking all of Germany rather than single items, visit PGLAF's information page about the German lawsuit.
If equals are subtracted from equals, then the differences are equal Subtraction property of equality. The stronger term " congruent " refers to the idea that an entire figure is the same size and shape as another figure.
The Pythagorean theorem states that the sum of the areas of the two squares on the legs a and b of a right triangle equals the area of the square on the hypotenuse c.
From the Preface: This book contains problems in solid geometry and is a natural continuation of Problems in Plane Geometry, Nauka, Moscow, Hence, with a very large proportion of beginners in Geometry, it depends mainly upon the form in which the subject is presented whether they pursue the study with indifference, not to say aversion, or with increasing interest and pleasure.Definition of a Triangle Triangle is a closed figure bounded by three straight lines called sides.
It can also be defined as polygon of three sides. Buy Avery's Plane geometry on galisend.com FREE SHIPPING on qualified ordersAuthor: Royal A Avery. Plane Geometry.
This book explains about following theorems in Plane Geometry: Brianchon's Theorem, Carnot's Theorem, Centroid Exists Theorem, Ceva's Theorem, Averys Plane geometry.
book Theorem, Desargues's Theorem, Euler Line Exists Theorem, Feuerbach's Theorem, The Finsler-Hadwiger Theorem, Fregier's Theorem, Fuhrmann's Theorem, Griffiths's Theorem, Incenter Exists Theorem, Lemoine's Theorem, Ptolemy's .Jun 06, · Book digitized by Google from the library of Harvard University and uploaded to pdf Internet Archive pdf user tpb.
Skip to main content. This banner Elementary plane geometry by Baker, Alfred. [from old catalog] Book from the collections of Harvard University Language English.
Book digitized by Google from the library of Harvard Pages: Scott, Foresman, - Geometry, Plane - pages. 0 Reviews.
Preview this book Plane Geometry Claude Irwin Palmer, Daniel Pomeroy Taylor Full view - Nov 23, · Before answering this perfectly, one would need to know your current ebook of geometric knowledge and what you hope to do with geometry.
I will try to address all the possibilities. If you have zero exposure to geometry, I’m actually not sure what.


Enter your subject of interest:
How long, in estimated reading minutes, would you like the response to be?
What specific time period(s) in the history of math are you most interested in learning about?
choose as many as you like
Are there any particular mathematicians or mathematical developments you are most interested in learning about from ancient history (before 500 AD)?
choose as many as you like
Should the response focus more on the cultural/societal aspects of math history or the mathematical concepts and discoveries themselves?
Do you have a basic, intermediate, or advanced level of prior knowledge about the history of mathematics?
The Ancient Greeks held mathematics in very high regard, seeing it as much more than just a practical tool. For them, the study of mathematics was an intellectual pursuit, a means of contemplating absolute truth and the fundamental nature of the universe.
The preeminent mathematician of ancient Greece was the legendary Pythagoras. He established a school of philosophy and mathematics on the island of Samos around 530 BC. Pythagoras and his followers believed that numbers and mathematical relationships were the key to understanding the cosmos. They searched for patterns in numbers, music, and nature, believing these revealed divine truths. The famous Pythagorean theorem relating the sides of a right triangle was discovered by the members of this school.
For the Pythagoreans, mathematics was inseparable from philosophy and even religion. By contemplating mathematical forms and theorems, they felt one could approach transcendent perfection and comprehend the mind of God. Unlike the Egyptians and Babylonians before them who used math for practical ends like trade and engineering, the Greeks were interested in math for its own inherent beauty and logic.
The Greek mathematician Euclid built upon the work of Pythagoras and others to systematize mathematical knowledge in his seminal work, the Elements. This thirteen volume set covered everything from geometry to number theory and solidified mathematics as a deductive system based on proven theorems and air-tight logic. Euclid's Elements would be used as the standard mathematics textbook for over 2000 years.
Archimedes was another great Greek mathematician who made breakthrough discoveries in geometry and calculus. He devised formulas to calculate the area and volume of spheres, cylinders, and other shapes. His insights were critical to the development of integral calculus centuries later. He also applied mathematics practically to devise ingenious machines and weapons to defend his home city of Syracuse.
For the ancient Greeks, mathematics was a central part of education and intellectual life. All free citizens were expected to have knowledge of basic mathematics, geometry in particular. Great philosophers like Plato and Aristotle incorporated mathematical concepts into their metaphysical speculations. The Greek intellectual reverence for mathematics allowed for major leaps in knowledge that shaped the course of Western thought. Their contributions ripple through the centuries, and much of our mathematical knowledge today traces back to the pioneering work of Pythagoras, Euclid, Archimedes and their Greek predecessors.
In contrast to the Greeks, ancient Chinese mathematicians viewed their craft as more practical in nature. Rather than contemplating abstract mathematical forms, they were focused on applying math to solve real world problems related to government administration, commerce, architecture and engineering. Despite this pragmatic focus, Chinese mathematicians made remarkable advancements in areas like algebra, geometry and trigonometry.
The ancient Chinese used mathematics extensively for calendar making, a crucial task for an agricultural society. Chinese calendars helped farmers plan their growing and harvesting schedules in accordance with the seasons. Calendars also had astrological and ritual significance, allowing prediction of lunar eclipses and determination of auspicious days. Mathematical astronomy helped Chinese astrologers create increasingly accurate calendars.
The decimal system used today worldwide owes its origin to ancient China. Chinese mathematicians realized the decimal system allowed easier calculation than using cumbersome fractions. By 4th century AD, Chinese manuscripts were using a full decimal system with a zero placeholder. This was several centuries before the zero was widely adopted in the West. The Chinese also developed the world's first decimal based currency during the Song Dynasty of the 10th and 11th centuries.
In architecture and construction, math enabled the ancient Chinese to build elaborate palaces, tombs, canals and defensive fortifications. They calculated the slopes and volumes needed for earthworks projects on a massive scale. During the Han Dynasty, mathematicians even described formulas for figuring out dimensions and distances in building construction.
The Chinese made early advances in algebra, finding methods to solve systems of linear equations with several unknowns. They analyzed polynomial equations and worked extensively with quadratic equations, which are essential to geometry and astronomy. Chinese mathematician Liu Hui even presented early iterations of the Pascal Triangle centuries before Pascal. This triangular array of numbers has many algebraic applications even today.
Ancient Chinese mathematicians made strides in trigonometry as well. They calculated values for spherical triangles, and applied trigonometric formulas to problems in surveying, engineering and astronomy. The famous astronomer and mathematician Shen Kuo used trig to fix errors in astronomical observation. Yu Xi is credited with discovering the tangent function during his geometric studies of the calendar.
While less theoretically inclined than the Greeks, ancient Chinese mathematicians made equally groundbreaking contributions. Their techniques for decimal numbers, algebra, trigonometry and computational methods provided an indispensable foundation for scientific progress and administrative efficiency in China. Practical in focus, but sophisticated in technique, Chinese math reached an apex during the Song Dynasty before gradually declining. The work of ancient Chinese mathematicians remains integral to modern mathematics.
The Mystical Allure of Numbers in Ancient Cultures
Numbers held a mystical significance in many ancient cultures beyond just their practical use in trade or engineering. The patterns and relationships observed in numbers were seen as having philosophical, religious, and even magical import.
The ancient Egyptians saw numbers as fundamental to the order of the universe. They believed numbers reflected the mind of the gods and held divine powers. The numbers 3, 4, 7, and 9 were considered sacred based on their mystical properties.
The Egyptians observed that the sides of a triangle with dimensions 3-4-5 would always form a right triangle. This "sacred triangle" was associated with their god Osiris. The pyramid shape constructed using these triangle proportions was seen as sacred geometry.
Egyptian preoccupation with numbers influenced their monuments. Pyramids were built with height and base dimensions carefully calculated using the phi ratio, meant to harness cosmic energies.
Obelisks were tapered to create an illusion of greater height, designed using ratios based on the "Golden Number" phi. This mathematical proportion was called the "number of Maat" and linked to spiritual harmony.
In Babylonian belief, numbers were connected to astrology and prophecy. They tracked the motions of celestial bodies, recording their positions based on regular cycles and mathematical calculations.
Through numerology, the Babylonians also used numbers to determine the best time to plant crops, go to war, or make other decisions. Certain numbers were seen as carrying positive or negative omens.
The Babylonians observed the 19-year Metonic cycle of the Moon's phases. This cycle linked lunar and solar calendars, and allowed prediction of eclipses. The ability to calculate such cycles was seen as mystical insight.
They also divided the ecliptic plane into 12 zodiac signs and noted the occurrence of lunar eclipses related to periodic repetitions of these 12 signs. These mystical number patterns were seen as conveying divine messages.
Ancient Indian mathematicians saw geometric patterns as manifestations of spiritual truths. They studied combinations of numbers as representations of the Hindu gods.
The earliest Indian mathematical text, the Shulba Sutras, focuses on precise geometric constructions of altars for rituals. The altar shapes carried symbolic meaning, with areas calculated using Pythagorean triples like 3-4-5.
These texts also contained approximation techniques for squaring the circle. Finding the value of pi was seen as unlocking cosmic wisdom.
The geometric diagrams used in ritual altar design were said to possess yantric power. Mandalas and lotus patterns were drawn using mathematical precision to harness spiritual energies.
Indian mathematicians saw numbers as the key to understanding cycles of time, space, and the rhythms of nature. By discerning these patterns mathematically, enlightenment could be attained.
Across ancient cultures, numbers were imbued with religious, philosophical and mystical significance. The perception of mathematical patterns and relationships in nature connected to how these cultures understood the universe and their place in it.
Though they differed in details, the Egyptians, Babylonians, Indians and other ancient peoples shared a numerological worldview. Their mystical approach to numbers aligned with broader beliefs about gods, spirits, and cosmic order. Mathematics provided the key to decoding divine truths.
Unifying Role of Mathematics in Antiquity
Mathematics played an integral role in the development of diverse ancient civilizations, serving as more than just a practical tool for architecture, trade, and administration. Though each culture related to math differently, mathematics became a unifying force that connected philosophy, religion, mysticism and culture across antiquity.
For the Greeks, math was an abstract discipline, studied for its inherent beauty and logic. Contemplating mathematical forms and geometric proofs was seen as a pathway to absolute truth. The order and perfection revealed in mathematics connected to Greek notions of cosmic harmony and a rational universe governed by divine principles. Intellectual giants like Pythagoras, Plato and Archimedes helped elevate mathematics to the center of Greek education and philosophy.
In China, math was valued for its concrete applications to state administration, commercial development, engineering and agriculture. Through sophisticated advances in algebra, trigonometry and computation, the Chinese created practical tools to manage a large empire and agrarian economy. While less theoretical than the Greeks, Chinese mathematicians made equally groundbreaking discoveries by analyzing real world problems mathematically.
Ancient cultures like Egypt, Babylon and India imbued numbers with mystical and religious significance. Sacred geometric patterns, numerological cycles of celestial events, and mathematical ratios found in nature all pointed to cosmic wisdom and divine truths for these cultures. Math provided insight into magical forces, prophecy, astrology and the link between man and the gods.
Despite their differences, for all ancient cultures math played a role beyond just practical calculation. It provided a means of expressing fundamental truths about order, patterns and relationships that defined their understanding of the universe. Every civilization had specialists devoted to studying mathematics, whether priest-astronomers decoding the gods' messages in numbers or philosopher-mathematicians distilling universal harmonies into theorems.
The universal language of mathematics connected these diverse ancient cultures. Trade between lands spread mathematical knowledge through shared numerical systems and problem solving techniques. Great works like Euclid's Elements synthesized and standardized mathematical learning between cultures. While the details differed, the incorporation of math into ancient religion, philosophy, mysticism and culture demonstrates its truly unifying worldwide impact. Mathematics provided an intellectual touchstone that transcended boundaries and shaped the trajectory of ancient thought. Its unifying legacy continues to resonate today.


Newton had made a mistake, and this lady figured it out
Émilie du Châtelet, portrayed in the documentary, Einstein's Big Idea (2005)
Émilie du Châtelet (1706-1749), one of the great female scientists of history, published many scientific papers, plus a French translation of Newton’s Principia.
However, her growing competence as a physicist led her to suspect that Newton had made a mistake in his theories on motion. According to Sir Isaac’s thinking, the energy of a moving object might be calculated simply as mass times velocity.
the substantially understated energy
But du Châtelet came to believe that this resultant, predicted energy had been substantially understated. She learned that the German mathematician Liebniz, a co-creator of calculus with Newton, contended that moving objects possessed, what he called, a “living force,” by which he meant to express, an unaccounted for extra energy in moving objects.
Critics called this “living force” a superstition, but du Châtelet believed that Liebniz was on to something. Liebniz insisted that the energy of a moving object could not be quantified simply by mass times velocity but required mass times velocity squared.
Squaring a number can take us to much larger numbers very quickly: for example, 5 + 5 = 10, but 5 squared, or 52, is 5 x 5 = 25.
Unwilling to relinquish her best judgment concerning the energy of motion, she discovered an experiment concerning lead balls dropped into a pan of clay. She adapted this to her purposes and found the data she needed.
A lead ball is dropped from a pre-determined height into a pan of clay. The force of the ball, from that particular height, makes a corresponding impression on the clay.
Next, a second lead ball is dropped from a higher height, which, according to Newton’s formulas, is calculated to double the speed of the first ball.
4 times the impact, not 2
Newton predicted that the force of the second ball would be 2 times that of the first ball. But Liebniz asserted that, if we double the speed of the second lead ball, the force of impact would not be twice that of the first ball, but 4 times the impact.
notice that the impression of the second ball, on the right, is
4 times as deep as the impression of the first ball, on the left
Liebniz had the correct view.
For example, a car traveling at a speed – let’s say, 20 mph – requires a certain distance to stop if full pressure is applied to the brakes. But if we triple the car's speed to 60 mph, now it's brought to a dead rest not in a duration 3 times that of the speed but 9 times as long; or 3 squared, 3 x 3, or 32.
In the mid-1700s, Émilie du Châtelet’s discovery was not widely accepted because the author was a woman, but also because the finding did not support the Newtonian worldview. The idea that there’s much more energy hidden in moving objects than we might suspect would need to wait for Albert Einstein, more than a hundred years later.
Editor's note: This non-acceptance of new correct ideas, due to servile homage paid to past luminaries, has always been a serious problem for our egoic world.
the substantially understated atomic energy
The “2” in Einstein’s famous equation, E=mc2, means that the amount of energy hidden in a quantity of matter becomes a function of mass times – not the speed of light, but – the speed of light squared.
This was Émilie du Châtelet’s discovery writ large.
The speed of light is not a small number: 186,000 miles/second. This seems impressive enough. One might think, as did Newton, that a simple multiplying of mass times speed should satisfy a definition of atomic energy. But, as it turns out, this formula doesn’t even come close.
The speed of light squared is 186,000 x 186,000, an enormous number; made all the larger by taking this product times the amount of mass in question. And this final number, let’s be clear, is equal to “E,” the “energy,” in E=mc2.
In other words, the atomic energy released from even a small amount of matter is utterly colossal and can destroy whole cities.
the world's first atomic blast-detonation, 5:29 AM, July 16, 1945
Einstein would have had another clue, not brought out in the documentary, that Nature favors the “squaring” function. Galileo determined that falling objects, released from a position of rest, cover a certain distance as time is squared.
Further, falling objects, near the Earth, such as the above falling apple...
do not fall at a constant rate, but plummet with an acceleration of 32 feet per second, per second; that is, acceleration is squared, denoted as 32 ft/s2. Objects will continue to accelerate in this manner until air resistance puts a brake on further increase.
There are other examples of this squaring phenomena; the work of Kepler's planetary motion comes to mind.
the hidden reserves of potency
Nature, in many contexts, seems to have a thing for squaring, suggesting hidden reserves of potency all around.


I need to calculate room square footages to give to our supplier to order flooring. I noticed when room areas are displayed along with the room labels, it is not calculated to the interior of the walls. Walls seem to be included, and some rooms seem to be different than others on how the calculation is done. Is there a way to adjust how these room calculations are done? Or do you have other advice on how to get this information for flooring square footages? The only options I have come up with so far are drawing a bunch of polylines in all the rooms or doing the math with the dimensions, and I was hoping for something easier.


Casinos That Offer the Best Probability of Winning
There are many varieties of casino games. Lots of people choose to visit their local casino for fun and excitement. However, many gamblers prefer to gamble at online casinos where there’s a variety of casino games to select from. One can also choose to gamble at a multiple casino venue, which might offer all sorts of casino gaming options.
Whenever a casino offers slots or pachinko games available for individuals to play, there are many different versions of these games available. The most popular version of slot machine gambling is straight slots. In this form of casino game, a player will spin the reels as rapidly as you possibly can in order to make just as much money as possible. The very same type of action is conducted with pachinko. While the exact same type of physical slot machine can be used for both games, whenever a player spins the reels in either slot machine, another payout will result.
Slots derive from the Binomial distribution and the numbers which are drawn are based on the probability distribution. The probability distribution runs on the binomial tree. In this way, the probability distribution shows a bell-shaped curve with two tails and a central mean. This distribution is referred to as the binomial distribution and is frequently used in the design of casinos.
Slots and pachinkos follow the same general rules with slight variations. When playing a casino game utilizing the binomial distribution, it is very important remember that standard deviations are employed instead of absolute values. Standard deviation may be the deviation of the common value from the normal distribution. This can be defined as the deviation of the mean value over the normal range. Standard deviations are calculated by firmly taking the standard deviation value and dividing it by the amount of successes in a random event.
There are many of other variations of casino slot games available to players. One of these is online slots, also called web-slots or online roulette. Online slots are not influenced by any local laws and there are a variety of web-based casinos available. The jackpot for online roulette and slots is normally much larger than the winnings on the actual machines. The jackpots for these games are constantly growing since most online casinos allow visitors to play for longer periods throughout the year.
The overall game of bingo includes a long history in the 더킹카지노 주소 United States. The overall game of bingo evolved from the early British English version of “sticks and stones” to the more contemporary version of “bingo” played at land-based bingo halls. One of the reasons for the boost in popularity of bingo is the perceived fairness of the game as compared to other casino game payouts. For example, the house edge – the money a player needs to win or lose before he loses his initial investment – for online bingo games is a lot smaller than the house edge for bingo at land-based venues.
Another version of the casino game that is available to players are blackjack and roulette, which require strategy to determine the best odds of winning. Blackjack and roulette are strictly luck based and no special skills must play these games. The two games are the only casino games that require a player to utilize any counting methods, including the traditional System or Blackjack Card Counting. Players can buy information about the best winning combinations for each game by using the Internet. An Internet casino that offers blackjack and roulette gets the best odds of winning the amount of money that is placed into the betting pool.
Video poker is another version of the casino game that’s available to players. Video poker originated in the late 90s whenever a amount of high rollers decided that it might be a fun way to win cash from their favorite casino game. Video poker is really a video gaming version of the planet renowned casino game called Caribbean Stud Poker. The Caribbean Stud Poker is played with exactly the same rules as do other versions of Caribbean Stud. When you play video poker at an online casino you can choose from a variety of high roller games and win cash simultaneously.


Setting OPEF’s Priorities
Setting OPEF’s Funding Priorities
In June 2018, OPEF conducted a strategic visioning retreat in collaboration with the District and parents.
After this retreat, OPEF tested these priorities through a district-wide parent survey. The Foundation received a tremendous 37 percent response from 1097 families who identified their top three priorities:
- Science, Technology, Engineering, Arts, and Math (STEAM)
- Reducing class size
- Additional counselors and counseling support


||Journal of Recreational Mathematics
Charles Ashbacher and Lamarr Widmer
Presently this journal is available in print format only.
We are working on providing the Journal of Recreational Mathematics electronically as well. If you would like to be notified as to our progress,
click here to sign up for free email alerts, just select Recreational Mathematics from the list and we'll keep you up to date on our progress.
The exciting side of numbers . . .
A journal devoted to the lighter side of mathematics. Featuring thought-provoking,
stimulating, and wit-sharpening games, puzzles, and articles that challenge
the mental agility of everyone who enjoys the intricacies of mathematics.
AIMS & SCOPE
The Journal of Recreational Mathematics is intended to fulfill the
need of those who desire a periodical uniquely devoted to the lighter side
of mathematics. No special mathematical training is required. You will
find such things as number curiosities and tricks, paper-folding creations,
chess and checker brain-teasers, articles about mathematics and mathematicians,
discussion of some higher mathematics and their applications to everyday
life and to puzzles solving. You'll find some occasional word games and
cryptography, a lot to do with magic squares, map-coloring, geometric dissections,
games with a mathematical flavor, and many other topics generally included
in the fields of puzzles and recreational mathematics.
The Journal of Recreational Mathematics is ideally suited for
use in any extracurricular math activity in high-school or junior college.
Its non-textbook approach will clarify in a recreational form many of the
abstract concepts wrestled with in formal classroom situations. The Journal
is tailor-made for anyone fascinated by numbers and number phenomena, from
seemingly simple arithmetic to involved calculus. The Journal of Recreational
Mathematics, a journal that is thought provoking and stimulating—offers
everyone interested in math a never-ending parade of the exciting side
of mathematics. Join your fellow math enthusiasts and subscribe to this
truly international Journal, with both subscribers and contributors
from over 25 countries throughout the world.
ABSTRACTED & INDEXED IN
- Academic Search Premier
- Book Review Index (BRI)
- H.W. Wilson
- International Bibliography of Book Reviews
- International Bibliography of Periodical Literature
- The Gale Group
A LOOK AT SOME RECENTLY PUBLISHED ARTICLES
Has a Salary Cap in the NFL Improved Competitive Balance? by Andrew K. Barriger, John W. Sharpe, Brendan P. Sullivan, and Paul M. Sommers
Park Elevation and Long Ball Flight in Major League Baseball by Jason M. Bloch, Kieran M. Coe, James K. Ebberson, and Paul M. Sommers
A Fourth-Order Digitally-Reversible Polylingual Bialphabetic Alphamagic Square by Lee B. Croft and Samuel Comi
Triangular Numbers with Pell Generators by Thomas Koshy
Square Catalan Numbers by Thomas Koshy and Zhenguang Gao
The Changing Racial Composition of Baseball’s All-Stars, 1950-2007 by Michael W. Winter and Paul M. Sommers
Studies in Magic Tours of Knight on 16 ´ 16 Board by Awani Kumar
Calculations by Katelyn Sack
On a Curious Property of the Number 37 by Elga Pakulis
Woodchucks by Steven Kahan
Exploring Sudoku by Andrew Incognito, Laura Hodge, and Collin Witt
Aaron–Bonds Pairs by Douglas E. Iannucci
An Interesting Family of Prime-Producing Polynomials by Bernard Haussy
Dr. Matrix on Little Known Fibonacci Curiosities by Martin Gardner
Philatelic Dissection Puzzle by Anil M. Nawlakhe
Closed Monochromatic Bishops’ Tours by Joe DeMaio
Some Words on Friday the Thirteenth by Richard Stein
An Arithmetic Alphametic Problem Solving Program by Timothy Garrett, Brian Jerome, Ellen Milbach, Andrew Reichenauer, and Charles Ashbacher
Paradox of Nontransitive Dice by Leyla Batakci and Kelly Singer
When Do NFL Quaterbacks Pass Their Prime? by Stefan G. Hrdina and Paul M. Sommers
The Discovery of a Periodic Table of the Prime Numbers by George A. Knudsen, Jr.
The Order 5 General Bimagic Square by Michael P. Cohen
New Curiosities Conerning Easter 2008 and the Digits of 23 by Owen O’Shea
New Curiosities on the Number 137 by Owen O’Shea
The Number 1729 by Owen O’Shea
Symmetric Games with Only Win/Loss Outcomes by W. F. C. Taylor
Harshad Numbers by Ed Bloem
© Copyright Volume 1 - 1968 through Volume 36 - 2007
|Baywood Publishing Company, Inc.
|Phone: 631 691-1270
||Fax: 631 691-1770
||Toll free order line: 800-638-7819


Descriptive statistics with SPSS (DIGITAL BOOK PDF)
- Brand: Editorial UCR
- Product Code: Elena Andraus Alfaro
- Availability: 100
The Descriptive Statistics with SPSS manual is an introductory guide that is intended as a guideline for all those interested in learning a little about the application of descriptive statistics in a Windows environment.
|File size||975 kB|
|Edition||1st ed. 2020|
|Format available||EPUB ebook|


September 18, 2023
Thomas A. Romberg, a professor emeritus with the UW–Madison School of Education, passed away on Sunday, Sept. 3, 2023, in Fitchburg, Wisconsin. He was 90 years old.
Romberg joined the UW–Madison faculty in 1966, and retired in 2005. Through his almost 40 years on the faculty he became an internationally recognized leader in mathematics education.
“Professor Romberg was a wonderful colleague, a thoughtful and effective teacher, and a brilliant researcher whose work made a powerful impact — on our campus, nationally, and internationally,” said School of Education Dean Diana Hess. “He was primarily concerned with what happened in mathematics classes — how teachers taught and what students learned, and the ways in which policy could advance both. The field of mathematics education is better and stronger because of his decades of leadership.”
Romberg’s research focused on young children’s learning of initial mathematical concepts, methods of evaluating students and programs, and integrating research on teaching, curriculum, and student thinking. Through his lifetime he published 30 books and over 300 research papers.
As a professional leader in mathematics education he chaired the Commission on Standards for School Mathematics for the National Council of Teachers of Mathematics from 1986 to 1985. From 1987 to 2002 he was director of the National Center for Research in Mathematical Sciences Education for the U.S. Department of Education, where he served as an adviser to three U.S. Presidents and their Secretaries of Education. He also represented the U.S. on several international commissions.
“His work on standards in mathematics education set the stage for some of the most robust national and international debates about the role of national standards in education and on their strengths and limits,” said UW–Madison Professor Emeritus Michael Apple, the former John Bascom Professor of Curriculum and Instruction and Educational Policy Studies in the School of Education. “Those of us who participated in these debates owe Tom a debt of gratitude for his openness to different opinions and his willingness to listen carefully, even when he disagreed.”
Romberg was also a former director of the National Center for Improving Student Learning and Achievement in Mathematics and Science, housed in the School of Education’s Wisconsin Center for Education Research, from 1996 to 1999.
While on the faculty at UW–Madison Romberg received a Faculty Distinguished Achievement Award, and also was named the Bascom Professor of Education. “Tom was a wonderful colleague,” said Robert Tabachnick, a professor emeritus in the Department of Curriculum and Instruction. “His colleagues and students appreciated his warm heart and the support and encouragement he was quick to offer his co-workers and his students, as well as his dry sense of humor.”
Romberg received numerous other awards and fellowships, including a Lifetime Achievement Medal from the National Council of Teachers of Mathematics for his contributions to mathematics and education.
To honor his life and legacy, Romberg’s family has requested that memorials be made to the Thomas A. Romberg Fellowship Fund through this link.


January 16 - 19
Monday: NO SCHOOL.
Tuesday: Math homework, Big Boom (board games).
Friday: Spelling test, Sledding party 8:30 - 10:00 for students who paid Cardinal coins for it.
A few ways you can help your child this week:
*Encourage them to read at home!!
*Practice basic addition and subtraction facts.
*If they have access, they can play math games at home to reinforce their skills. Check out the RG Math Games page!
Reading: This week, students are working on making inferences from texts as they read. We are also comparing and contrasting two fictional stories.
soup, blue, glue, clue, blew, group, threw, soon, zoo, classroom
Spelling City: https://www.spellingcity.com/users/cassandraspanovich
Writing: Students are learning about writing informational reports, including researching and taking notes. They will begin to find books on an animal of their choice. We are also starting cursive!
Math: We are starting a new unit on 2-digit addition and subtraction. The students will be learning multiple strategies to add and subtract. These strategies will be explained to parents at conferences. Ask your child to explain the strategies they are learning!
Science: We are learning about solids and liquids.
It's hard to believe we are already in the 3rd quarter of our school-year! We have been having a lot of fun learning in Room 123, and I love working with your children every day. Please don't hesitate to email or call with any questions, comments, or concerns.
|Contact: Cassie Spanovich|


Science, technology, engineering, and mathematics (STEM) education is most effective when students understand how these concepts apply in the real world. Learning how actual scientists, engineers, and other professionals use STEM concepts to solve complex problems helps bring these ideas to life and answers the age-old question, “Why do we have to learn this?” What’s more, connecting STEM concepts and careers should begin in elementary school, when students’ natural curiosity is greatest. Not only does this make STEM education more concrete for students; it also exposes them to possible career paths at a young age, which expands their vision for what is possible in life. Download this white paper to learn how to link STEM concepts to careers in the early grades, along with three keys to success.
Please I want to join the STEM SSP


MATH Standards for High School, MODELING
Modeling links classroom mathematics and statistics to everyday life, work, and decision-making. Modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. When making mathematical models, technology is valuable for varying assumptions, exploring consequences, and comparing predictions with data. Examples include:
- Modeling savings account balance or investment growth.
- Analyzing risk in situations such as extreme sports, [or financial investing]
- Use probability to evaluate outcomes of decisions
CCSS.MATH.CONTENT.HSS.MD.B.5. Using Probability to Make Decisions
Weigh the possible outcomes of a decision by assigning probabilities to payoff values and finding expected values.
CCSS.ELA-Literacy in Social Studies.RH.6-8.1
Cite specific textual evidence to support analysis of primary and secondary sources.


The voltage gain magnitude equation for a second order low pass Butterworth response is given by. where. A F = 1+ R F /R 1 = pass band gain of the filter. f = frequency of the input signal, in Hz. f H = High cutoff frequencies, in Hz. The normalized Butterworth polynomials are given in Table 15.1. where s = jω and coefficient of s = 2 k, where. The voltage gain magnitude equation for a second order low pass Butterworth response is given by. where. A F = 1+ R F /R 1 = pass band gain of the filter. f = frequency of the input signal, in Hz. f H = High cutoff frequencies, in Hz. The normalized Butterworth polynomials are given in Table 15.1. where s = jω and coefficient of s = 2 k, where. Cadastre-se e oferte em trabalhos gratuitamente. 2021. 8. 6. · The amplitude of this point is 1/√2 of the maximum voltage. The maximum transfer function is at point A where V R =V s, the maximum power that can be achieved at the output. The power will be less at any other point within the graph shown as the gain is less than 1. Equating this transfer function to Eq. (1-3) gives TLP(0) = 1, ωo = 106 rps, and Q=1/ 2 . Substituting these values into Eq. (1-5) gives p1,p2 Standard, Second-Order, Low-Pass Transfer Function - Frequency Domain The frequency response of the standard, second-order, low-pass transfer function can be normalized and plotted for general application. For instance, in the link I posted, the transfer function for the filter ends up being: H ( s) = − s R 1 C s 2 + 2 R 3 C s + 1 + R 1 / R 2 R 1 R 2 C 2. from which they deduce based on its similar form to the original equation I posted what ω 0, Q and other variables are. transfer-function active-filter laplace-transform band-pass. . See full list on allaboutcircuits.com. 2022. 5. 29. · This page will cover the derivation of the transfer functions of low-pass and high-pass Butterworth filters.Butterworth filters are designed to have a very flat frequency response in the passband. ... Up until now, we only looked at the low-pass Butterworth filter.There's also a high-pass version:. Op-amp Tutorial Includes: The. May 25, 2016 · One possible implementation (using transposed Direct Form II) for this transfer function is shown below. For example, see below digital notch filter with a = .99 and ω n = 0.707. (Frequency axis is normalized where 1 = f s / 2. Update: Please see further details including the closed form equation for the bandwidth of the notch. nd order high pass filter's transfer function would behave when f << fc?) All 1st order high pass filters have the same shape when plotted this way. The transition from the region of little attenuation, f >> fc, to the region of strong attenuation is not very sharp with this type of filter, the transition region being. Butterworth High-pass, Bandpass and Bandreject Filters 𝑅 Setting C=1 ( ) 2 For the variables 2 Observations The high-pass circuit is like the low-pass with the capacitors and resistors switched The prototype high-pass filter transfer function can be obtained from the low-pass by replacing s with 1/s.. 2022. 6. Indeed, if the given digital filter transfer function is lowpass then Table 4 gives the required transformations for the target filter transfer function. All frequencies are taken to be normalized, i.e., a typical value is given by θ = ω Δ t where ω is the angular frequency (in rad s −1 ) and Δ t is the sampling period (in s). High Pass Filter Passive Rc Filter Tutorial. Solved Problem 1 Determine The S Domain Transfer Function. Understanding The First Order High Pass Filter Transfer. Op Amp High Pass Filter Cutoff Frequency Derivation. Rl High Pass Filter. Rc Low Pass Filter Single Pole Magnitude Phase And 3db Frequency. Active High Pass Filter Op Amp High Pass. A low-pass filter passes frequencies below a certain cutoff frequency and attenuates those beyond that frequency. RC low-pass filter. The first circuit we shall analyze is that of an RC low-pass filter, as shown in the figure above. Before launching into a mathematical analysis, we can deduce some of the electrical properties by visual. The reason this product of separate "transfer functions" (what I called tf1 and tf2) works, whereas the product of the separate high and low pass transfer functions doesn't give the correct answer, is that tf1 was calculated taking into account the loading effect of the following high pass section. Give it a try and post your results here. Analyzing this transfer function uses very similar ideas, there are just more terms to deal with. Here's a guide. Filling in the gaps (in the same spirit as the low-pass and high-pass lters above) is left as an exercise. Low-frequency asymptote. For the low-frequency asymptote, take f!0 as usual, so that 1 ˛Bfand 1 ˛Cf. High-frequency. This type of filter acts as a bandpass filter. The op-amp increases the amplitude of the output signal and the output voltage gain of the passband is given as 1+R2/R1, which is the same as the low pass filter. Transfer Function. To derive the high pass filter transfer function, we will consider a passive RC HPF circuit as shown above. 5. 29. · This page will cover the derivation of the transfer functions of low-pass and high-pass Butterworth filters. Butterworth filters are designed to have a very flat frequency response in the passband. ... Up until now, we only looked at the low-pass Butterworth filter. There's also a. The problem with that approach is that low pass and high pass filters with magnitude responses that are optimal. 2022. 6. 17. · If Ωu is the desired passband edge frequency of the new low pass filter, then the transfer function of this new low pass filter is obtained by using the transformation s.


Chennai Mathematical Institute Internships in Computer Science
Summer internships in Computer Science
Duration: Internships in Computer Science should be for at least one month and could be as long as a semester.
Value: Return train fare by Sleeper Class. Accommodation will be provided to students, usually in the hostel on campus. Students will be paid a fellowship. They are expected to pay for their food in the hostel from this fellowship.
Eligibility: Students should have a background in programming, and preferrably some exposure to algorithms and/or automata theory. Normally, CMI does not offer internships to students before the end of their second year of college/university.
How to apply for internships at CMI: Use this online form http://www.cmi.ac.in/~csinternships/appform/form.html, to apply. Applicants should have an email address. Make sure your email address is entered correctly in the form as the Institute will contact applicants through email only.
Chennai Mathematical Institute (CMI), is a centre of excellence for teaching and research in the mathematical sciences. It was founded in 1989 as a part of the SPIC Science Foundation, funded by the SPIC group in Chennai.
Chennai Mathematical Institute is a university under Section 3 of the UGC Act 1956. It is recognized both within the country and abroad
as one of the important centres in India for research and teaching in mathematical sciences.
The main areas of research at CMI are Mathematics, Computer Science and Physics. In addition to a PhD programme, the Institute conducts BSc programmes in Mathematics and Computer Science as well as Physics. CMI also conducts MSc programmes in Mathematics and Computer Science.
The Institute receives substantial support for its activities from the Department of Atomic Energy (DAE), through the National Board for
Higher Mathematics (NBHM).
Chennai Mathematical Institute
H1, SIPCOT IT Park, Siruseri
Kelambakkam 603 103, India
(044) 6748 0900, (044) 2747 0226–0229,
(044) 3298 3441/3442


How to Win at Slot Machines
The slot is one of the best areas to shoot the puck because it offers the best chance of scoring without deflection. In addition, a straight-on view of the net gives an advantage in terms of accuracy and placement. The low slot also provides a good place for a wrist shot. In contrast, defenders often establish the slot as no man’s land by laying big hits to wingers.
Probability of hitting a particular combination of symbols on a slot machine
The probability of hitting a particular combination of symbols on slot machines varies according to the pay table and the random number generator (RNG). The RNG is a computer program that cycles through thousands of numbers per second. Each symbol on the reel is corresponding to one of those random numbers. Early slot machines were simple and relied on simple math to determine the payoff. Modern machines use sophisticated mathematical algorithms to determine the probability of a specific combination.
Random number generators power slot machines
Slot machines make use of Random Number Generators (RNGs) to pick the winning combination of numbers. They do so thousands of times a second. Every spin is decided by an algorithm that provides instructions for generating random numbers.
Three-reel machines are more reliable than five-reel machines
In theory, three reel slot machines are more reliable than five reel machines. A three-reel machine has three fixed reels. The number of combinations can vary from one machine to the next, but on average, 75 to 95 cents of every dollar you spend is returned to you over the life of the slot. But there is no way to guarantee that a three-reel machine will have a higher payout rate.
Video slot machines encourage players to play multiple “lines”
Multi-line slots allow players to place multiple bets on the same payline. These paylines are made up of visible symbols that must match in order to produce a winning combination. A traditional three-reel machine may have one payline, but video slots typically offer nine, fifteen, twenty-five, or even as many as 1024 paylines. Multi-line machines allow players to place variable amounts of credits on the paylines. The higher the credits, the higher the payout.
Scatter symbols are a type of symbol on a slot machine
Scatter symbols on a slot machine trigger bonus rounds and free spins. They can also trigger frequent mini-games that can help you increase your winnings. However, different types of scatter symbols come with different winning schemes. These symbols are categorized according to their methods of triggering a bonus round and how much they pay out.
Poker machines do not have spinning reels
Poker machines do not have spinning reels, but that doesn’t mean that you can’t play them. Usually, a player can choose the number of lines they want to play. The minimum bet is one line across the reels, but if they have more money they can play additional lines above and below the main line, or diagonal lines across the reels. Players with multiple bet options usually win the highest jackpot only if they place the maximum bet.


MathConcept Learning Center (Diamond Hill)
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Shop No.: G108-G109
Telephone: 2882 1682
Opening Hours: 09:00 - 19:00 (Mon - Sat) / OFF (Sun & PH)
Incorporated by a group of elite mathematicians and mathematics educators, renowned university education professional, best-selling textbook author, subject teachers and education management professionals, MathConcept has been dedicated in providing all-round learning experiences in mathematics. MathConcept was first founded in Olympian City of Hong Kong. We currently have several learning centers located at different districts, with more than 20,000 students in the region. Till now, MathConcept has developed a sophisticated base of teaching material, with more than 100,000 pages of courseware and 104 publications, satisfying the needs of both local and international school students in Hong Kong covering curriculums from kindergarten to various high school levels.


Rolf Möhring (Technische Universität Berlin)
Abstract: This lecture will present an overview of the theoretical background and the available algorithmic tools for computing good and delay resistant periodic timetables.
The main model is the periodic event scheduling problem (PESP) introduced by Serafini and Ukovich, which interprets periodic timetables as periodic potentials of a digraph. This model contains graph coloring as a special case, which illustrates the computational difficulty of periodic timetabling. Periodic potentials are closely related to the cycle space of the underlying graph, and finding a “good” integral basis of this space is one of the most important techniques for reducing the feasibility domain and finding good solutions.
Computing delay resistant requires a combination of the PESP model with techniques for robust optimization. As classical models of robustness (Bertsimas, Sim, Ben-Tal) are not suited for the PESP, we have developed a more general model of recoverable robustness that extends the classical concept of robust optimization and overcomes its inherent problem of being over-conservative. We will discuss this new model and demonstrate its scope on the PESP and other optimization problems.
Mark Overmars (Department of Information and Computing Sciences, Universiteit Utrecht)
Abstract: Path planning is a central problem in virtual environments and games. When computer-controlled characters move around in virtual worlds they have to plan their paths to desired locations. These paths must avoid collisions with the environment and with other moving characters. Also a chosen path must be natural, meaning that it is the kind of path a real human being could take. The algorithms for planning such paths must be able to handle hundreds of characters in real-time and must be flexible.
In this talk I discuss recent developments in path planning algorithms for games. In particular I focus on the Corridor Map Method. The method is fast and flexible and the resulting paths are of high quality. As will be shown the method can plan paths for crowds of thousands of characters in real time.
Eytan Ruppin (Schools of Computer Science & Medicine, Tel-Aviv University)
Abstract: A prime goal of the emerging field of Computational Systems Biology is to develop genome-scale network models of major cellular processes. One domain in which considerable progress has been made is metabolism, denoting the processes that degrade and construct cellular metabolites via enzymatic reactions, a central tenant of life. This talk will review a few computational constraint-based methods that have currently been employed to study large-scale metabolic models of numerous organisms, and briefly outline the main achievements obtained. I shall then describe the human metabolic model that has been published last year, and proceed to present our recent work on developing and testing metabolic models of specific human tissues, including the brain, heart, liver and kidney. Finally, I shall describe the first in silico investigation of Inborn Error Metabolic disorders, generating predictions of metabolic profiles in biofluids for hundreds of these diseases, and the computational and conceptual challenges that lay ahead. No prior Biological knowledge will be assumed.
[Joint work with Tomer Shlomi, Moran N. Cabili, Markus J. Herrgård and Bernhard Ø. Palsson]
David P. Williamson (Cornell University)
Abstract: In incremental optimization problems, choices we make in the future are constrained by those we have made in the past. The canonical example of this is the incremental k-median problem, a variant on the k-median problem, introduced by Mettu and Plaxton. If we have already opened k facilities, and now wish to open k' > k facilities, we may not close facilities we have already opened. Hence the output of the incremental k-median problem is simply a sequence of all the facilities; if we wish to open k facilities, we open the first k in the sequence. Somewhat surprisingly, Mettu and Plaxton showed that it is possible to find a good sequence, in the sense that for any k, opening the first k facilities is within a constant factor of the best possible solution to the k-median problem.
In this talk, I will show a very general approach to incremental problems that are conceptually simple and leads to the best known performance guarantees for many of these problems, including hierarchical clustering problems. I will also discuss some recent experimental work that shows that these algorithms perform much better in practice than their theoretical performance guarantees. I will conclude with some open questions prompted by both the theoretical and the experimental work.
Leslie G. Valiant (Harvard University)
Abstract: We propose a bridging model aimed at capturing the most basic resource parameters of multi-core architectures. We suggest that the considerable intellectual effort needed for designing efficient algorithms for such architectures may be most fruitfully pursued as an effort in designing portable algorithms for such a bridging model. Portable algorithms would contain efficient designs for all reasonable ranges of the basic resource parameters and input sizes, and would form the basis for implementation or compilation for particular machines. We show that for several fundamental problems, namely matrix multiplication, Fast Fourier Transform, and sorting, algorithms do exist that are optimal in a defined sense, for all combinations of input size and parameter values for this model.


Weight And Height Converter Body Mass Index Calculator
Converts your weight and height into Imperial or Metric measurements with a single click.
1. Start with Metric or Imperial.
2. Height will always be displayed in feet and inches - inches over 11 are translated into feet and inches.
3. Your results are instantly displayed. Just input a number.
4. After you input figures for both height and weight, a calculation for Body Mass Index (BMI) is displayed showing ideal weight range and percentage under or overweight.


From the Register-Mail:
Dennis Schneider, professor of mathematics at Knox College, has been named winner of the 2009 Caterpillar Foundation Faculty Achievement Award. The award is presented annually to a member of the Knox faculty for outstanding achievements in teaching, research, creative activity and service.
S.C. “Sid” Banwart, vice president of the human services division of Caterpillar Inc., presented the award at Knox’s 2009 Commencement on June 6. “For his entire 36 years on the faculty, Professor Schneider has maintained high standards of rigor and innovation, as he taught and provided leadership for the program in mathematics,” Banwart said.


Many magic tricks use mathematics to fool the audience
Let's start with a magic trick!
- Choose any number
- Add 4 to your number
- Now multiply by 2
- Now take away 2
- Divide by 2
- Now take away the number that you first thought of
I bet I know your final answer...
Is it ...
Try this trick on your friends to test your mind-reading ability. Actually, you're not really doing magic, you're doing algebra, a branch of mathematics that goes back thousands of years.
In this unit, you will learn how to use symbols to stand for unknown numbers, which you will then find. You will also learn how to form your own mind-reading tricks.
- total file downloads...13022
- total number of shared resources...2000


I have been busy preparing and teaching mathematics lessons for the entire week. My mentor has not given myself a lot of feedback; but only to say she is happy with the lessons and loves my resources. I am hoping she will give more feedback next week, so I can produce a good reflection for my assignment.
As well as teaching mathematics this week, I have also been taking literacy groups and today I was involved in Under 7’s day, which was a fantastic experience for the students and very well organised.
I am now busy preparing mathematics literacy lessons for next week.


One problem with the top 1% simplification is that people who have college degrees aren't experiencing high unemployment. So it would be equally fair - and by that I mean equally illogical - to conclude that highly educated people are stealing the nation's wealth from less educated people. That's a bumper sticker you won't see.I would also be willing to bet that the average math skills of the people who are doing well in this economy are better than the average math skills of the people who are suffering. In other words, the Occupy Wall Street protesters are probably comprised of more psychology majors than engineering majors. But no one is suggesting that people who are good at math are stealing the nation's wealth from people who are not. That's not a catchy slogan.


I took a child development class the last half of my senior year of high school. On the last week of school, my teacher brought out sheets of paper with sudoku puzzles on them. I didn’t know how to play, so she and a couple others told me how to play and from there on out, I was hooked.
The rules are simple: There are 9 rows both vertical and horizontal and 9 squares within the big box. The player needs to have the numbers 1-9 in each horizontal and vertical row and square but the same number can’t be in the same row or square. For example if you put 9 in the upper right hand corner, no other 9 can be in the same square or vertical or horizontal row that this 9 is in. By the time you fill in all the blanks each row and square should have all the numbers once. The rules are simple but can get difficult especially if multiple numbers can fit in one spot.
That’s why they call it a logical puzzle because you have to think about where you’re placing all the numbers. The game originated from Japan (as well as many other puzzles.)
I’d taken a break from playing sudoku for a while, and have only recently picked it up again. When we were in our cruise last year, a Japanese girl working for the line hosted sudoku puzzles in the morning and the first 3 people who filled in the puzzle in 15 minutes or less won a prize. Of course I didn’t win but it got me back in the game again.
Now I’m working on them again I’m a book and I’m finding that I getting a system down. I’m not fast but I’m getting better. I’ll have to get more games once I finish this one up.


Supporting excellence in middle school mathematics since 1986
MATHCOUNTS is a national enrichment, coaching and competition program that promotes middle school mathematics achievement through grassroots involvement in every U.S. state and territory since 1983.
The Chester County Chapter in Pennsylvania has been holding the MATHCOUNTS competitions since 1986.
Helping Students Learn, Grow, and Achieve
Our competitions have challenged sixth, seventh and eighth grade students from 47 public, private and religious schools in the County. These students have a passion for mathematics and many move on to careers in important fields such as accounting, business, engineering, mathematics, science, teaching and technology.
Event: September Mathcounts
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HAPPY LEAP DAY to you!!!
Wednesday, FEBRUARY 29, 2012 - It's still Leap Day!
I was reading about people whose birthdays are February 29th. They are told to pick February 28th or March 1st as their birthday because the computers can't recognize February 29th.
What a bunch of leaping crap. Really, computers that can do trillions of calculations per second, can't figure out how to incorporate one single, simple, SPECIAL day into their programs. That's just being lazy. Not to mention rude.
Here's what I found out about Leap Day/Leap Year from Time and Date.com:
Leap Years are needed to keep our calendar in alignment with the Earth's revolutions around the sun. It takes the Earth approximately 365.242199 days – or 365 days, 5 hours, 48 minutes, and 46 seconds (a tropical year) – to circle once around the Sun.
However, the Gregorian calendar has only 365 days in a year, so if we didn't add a day on February 29 nearly every 4 years, we would lose almost six hours off our calendar every year. After only 100 years, our calendar would be off by approximately 24 days!
Julius Caesar introduced Leap Years in the Roman empire over 2000 years ago, but the Julian calendar had only one rule: any year evenly divisible by 4 would be a leap year. This lead to way too many leap years, but didn't get corrected until the introduction of the Gregorian Calendar more than 1500 years later.
In the Gregorian calendar 3 criteria must be met to be a leap year:
- The year is evenly divisible by 4;
- If the year can be evenly divided by 100, it is NOT a leap year, unless;
- The year is also evenly divisible by 400. Then it is a leap year.


I confess, I’m a data junkie. I’ve gathered data for various things, including my power usage over the years, and plotted it on graphs just to compare long-term usage in a visual manner. It’s the numbers that get me. I love math and working with numbers. I’m also a visual person.
Yet, I don’t have time to plot everything I’m interest in to compare long-term usage or effects. Thankfully, for VAERS data, I don’t have to.
Meet Dr. Jessica Rose, a Canadian who has a background in immunology, applied mathematics, computational biology, biochemistry and molecular biology. She recently completed a VAERS data analysis and presented it to the World Council for Healthy on October 11, 2021.
To learn about her findings regarding the vaccine, watch the video with a slide show here: Presentation of VAERS data to the World Council for Health.
Knowledge is power. Let’s keep informed.