Evelyn Lamb sur Twitter : "(Last tweet refers to recently disproved triangulation conjecture... Geometry - Tessellations and Symmetries. A tessellation (or tiling) is a pattern of geometrical objects that covers the plane. The geometrical objects must leave no holes in the pattern and they must not overlap. You should be able to extend the pattern to infinity (in theory). You make a tessellation by starting with one or several figures and then you rotate, translate or reflect them; or do a combination of transformations, in order to get a repeating pattern. If you only want to use one regular polygon to make a tessellation, there are only three possible polygons to use: triangle, square and hexagon. Click on the triangle and square in the example above to see the other two possible tilings of regular polygons.
Starting with a tiling of regular polygons, you can distort it (as shown above). The triangle tiling is distorted to a tiling of two different tiles. On the page GeoGebra Tutorial - Symmetries there is a description of how to make a tessellation using GeoGebra. Symmetries Drag the red point to make a painting! Make Hyperbolic Tilings of Images.
The loaded image will be cropped to the centered hyperbolic polygon. Repeated hyperbolic reflections of the centered polygon make up the tiling. The option generate large generates a tiling that is larger than the image shown on the screen. The default scale factor for an enlarged tiling is four, this is a length factor. Another scale factor can be chosen below. Chrome may crash when trying to download a large image - "Aw, Snap! " Larger tilings take longer time to generate, mostly since the edge of the tiling gets finer. If change first tile is clicked, the rendering of the first tile will cycle through "no distortion", "Klein distortion", and "polynomial distortion". The hyperbolic tiling The tiling is made of regular hyperbolic polygons with sides. is the number of polygons meeting at each corner.
When a so-called Poincaré disc is used to model hyperbolic geometry, the entire universe is inside a circle . Polynomial distortion Pick a point inside the Euclidean polygon. When then. Fabienne Serrière sur Twitter : "91.8% funded, 49 hours to go! Each scarf is different and comes with source code #math #knit. KnitYak: Custom mathematical knit scarves by Fabienne "fbz" Serriere. David Wees sur Twitter : "Example of the triangle inequality in french fries. #mathchat #geomchat #beingsillychat...
Mathnasium sur Twitter : "Snowshoes + math = stunningly beautiful snow art! #mathisbeautiful #mathart. Snowshoes + Math = Chillingly Beautiful Snow Art. Replicakill : Of course, many of you already ... Does one have to be a genius to do maths? « What’s new. Plausible Values. Plausible values were first developed for the analyses of 1983-84 NAEP (National Assessment of Educational Progress) data, by Mislevy, Sheehan, Beaton and Johnson, based on Rubin's work on multiple imputations. Plausible values were used in all subsequent NAEP surveys, TIMSS and now PISA. According to air.org: Plausible values are imputed values that resemble individual test scores and have approximately the same distribution as the latent trait being measured.
Plausible values were developed as a computational approximation to obtain consistent estimates of population characteristics in assessment situations where individuals are administered too few items to allow precise estimates of their ability. Plausible values represent random draws from an empirically derived distribution of proficiency values that are conditional on the observed values of the assessment items and the background variables.
What Plausible Values Are Why We Need Plausible Values So why are plausible values used? . NSA misuse of mathematics: Secret formulas and backdoor cryptography. Photo by Kerem Yucel/iStock/Thinkstock Recently, I co-authored and published a math paper that solved a 15-year-old mystery. But, unlike a book or a gadget, the work cannot be copyrighted or bought and sold. In fact, my co-author and I have made our paper available for free, for the whole world to see, on arXiv, an online depository of scientific articles. This inherent democracy has always been the mark of mathematics: It belongs to us all, even if people are not aware of it. Mathematicians don't expect to be paid for their discoveries; we do math because we want to understand how the world works. This principle has deep roots in history as well as in legal systems.
No one can own mathematical knowledge; no one can claim ownership of a mathematical formula or idea as a personal possession. A scientific truth, or the mathematical expression of it, is not a patentable invention. ... Courtesy of Basic Books Secrecy in cryptography is nothing new. Mathematics is a great equalizer. \(1111_{2}\) Things To Say When Teaching A Programming Course | Math Misery? If you are teaching a programming course (or any course, really), here are some opening statements for you to share with your class on the first day: In order to get the correct answer, you must ask the correct question.
Please speak up and ask if you don’t understand something. The professor is not a mind reader. The professor is not perfect. If you notice something that doesn’t seem correct, say something. SVG Hex Grid Generator. SVG hex grid generator This script generates hex grids in SVG (scalable vector graphics) format. Grids are transparent so they can be overlaid on maps. Hex numbering is optional and (somewhat) customizable. Label format. The format string defines the label that will appear on each hex if "Enable labels" is selected. If a number is placed between the "%" and the following letter, then the value will be zero-padded to fill that many characters.
Guides. This project is under development - see here for more information. First proof that infinitely many prime numbers come in pairs. Maggie McKee Mathematician Yitang Zhang has outlined a proof of a 'weak' version of the twin prime conjecture. It’s a result only a mathematician could love. Researchers hoping to get ‘2’ as the answer for a long-sought proof involving pairs of prime numbers are celebrating the fact that a mathematician has wrestled the value down from infinity to 70 million. “That’s only [a factor of] 35 million away” from the target, quips Dan Goldston, an analytic number theorist at San Jose State University in California who was not involved in the work.
“Every step down is a step towards the ultimate answer.” That goal is the proof to a conjecture concerning prime numbers. Those are the whole numbers that are divisible only by one and themselves. The twin prime conjecture says that there is an infinite number of such twin pairs. The problem has eluded all attempts to find a solution so far. But a referee report from the Annals of Mathematics, to which Zhang submitted his paper, suggests he has. Resonance Phenomena in 2D on a Plane. Synchronized Ferrofluid Sculptures. Numerical analysis of Chladni figures. Watch how mercury completely flips out when it's blasted by sound.