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88 posts tagged with Geometry.

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## Uses of inedible cheese

Cheese Slope Mosaics: how to arrange not-quite-triangular LEGO pieces into impressive patterns, projects, scenes, and everything under the sun.

## Animated math

Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]

## xEuclidx

Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods. [more inside]

## Babylonian (Pre)Calculus!

Signs of Modern Astronomy Seen in Ancient Babylon - "Scientists have found a small clay tablet with markings indicating that a sort of precalculus technique was used to track Jupiter's motion in the night sky." [more inside]

## A Beautiful Theorem Deserves a Beautiful Proof

Douglas Hofstadter presents a proof Napoleon's theorem (on equilateral triangles constructed on the sides of another triangle), in the form of a sonnet. (Part of a longer talk; the link should take you to 34:18 in the video.)

## /r/gonwild

"Loadingicon are small, trippy-looking color-limited .gifs that would make good or at least interesting animated icons or loading screens.

Gifs posted should be a closed loop, and animated either by hand or computer.

Gifs drawn from film, television, or other video sources are not allowed. Reposts or posts that otherwise aren't a good fit may be removed at the mods' discretion.

[more inside]

Gifs posted should be a closed loop, and animated either by hand or computer.

Gifs drawn from film, television, or other video sources are not allowed. Reposts or posts that otherwise aren't a good fit may be removed at the mods' discretion.

[more inside]

## Inspired by mathematical theorems or open problems...

Conveyer Belt Font. More mathematical and puzzle fonts/typefaces you can play with in your browser. Read about them in the article Fun with Fonts: Algorithmic Typography. [PDF]

## New Pentagons

Mathematicians discover a new type of pentagon that can cover the plane leaving no gaps and with no overlaps. It becomes only the 15th type of pentagon known that can do this, and the first discovered in 30 years. [more inside]

## Thanks, Common Core.

Thanks, Common Core. Physics blogger Chad Orzel writes about the way kids do math now. (Spoiler: he likes it.) [more inside]

## No Pentagons

Imperfect Congruence -

*It is a curious fact that no edge-to-edge regular polygon tiling of the plane can include a pentagon ... This website explains the basic mathematics of a particular class of tilings of the plane, those involving regular polygons such as triangles or hexagons. As will be shown, certain combinations of regular polygons cannot be extended to a full tiling of the plane without involving additional shapes, such as rhombs. The site contains some commentary on Renaissance research on this subject carried out by two renowned figures, the mathematician-astronomer Johannes Kepler and the artist Albrecht Dürer.*[more inside]## Alexander Grothendieck

Alexander Grothendieck, who brought much of contemporary mathematics into being with the force of his uncompromising vision, is dead at 86, some twenty-five years after leaving academic mathematics and retreating into a spiritual seclusion in the countryside. "As if summoned from the void," a two-part account of Grothendieck's life, from the Notices of the American Math Society: part I, part II. [more inside]

## A digital replica of the classic Spirograph toy

Do you have fond memories of afternoons spent making geometric patterns and designs with your Spirograph? If so, enjoy Inspirograph, a digital version. [more inside]

## THERE IS ONLY ONE MAGIC HEXAGON

## Geometry in motion

Bees & Bombs is a tumblr of hypnotic GIF animations programmed by Dublin-based physics student Dave Whyte

## shaky cam + time lapse + inferred geometry + smoothed path =

## The Foehr Reef

The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short video shows its beauty [alternating English and German audio]. PDFs with pictures.
"The Crochet Coral Reef is a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. [more inside]

## musical mathematical journeys

Trio for Three Angles (1968) is one of many beautiful acclaimed visually-oriented short films with music by mathematical filmmakers Bruce and Katharine Cornwell, some animated by hand and some using early digital technology. It inspired three sequels: Similar Triangles (1975), Congruent Triangles (1976), and Journey to the Center of a Triangle (1978) (previously). [more inside]

## Tool Unlocked: Equilateral Triangles

## Sphere Factory

## "I really like polyhedra."

Polyhedra and the Media - On the new polyhedra of Schein and Gayed, and mathematical journalism.

## Geogebra

Geogebra is an interactive geometry tool which started as a free clone of Geometer's Sketchpad, but is now also an algebra, statistics and calculus tool. It is available for download for Windows, Mac, Linux, iOS and Android, or as a web app. [more inside]

## Visual Patterns.

Visual Patterns. Here are the first few steps. What's the equation?

## The Hierarchy of Hexagons

The Hierarchy of Hexagons.

*School geometry seems to me one of the most lifeless topics in all of mathematics. And the worst of all? The hierarchy of quadrilaterals.*## Dynetzzle

A standard 6 sided die is a cube. It has eleven nets. The sum of the numbers on opposite faces of a die is 7. [more inside]

## Money

## Papercraft project blog Paper Matrix

Paper Matrix is a blog that gives instructions for cool papercraft objects, "reinterpreting the Danish tradition of woven paper hearts and ornaments." Cut paper in the prescribed ways and weave it together carefully to make a mobile of colorful hot air balloons, gorgeous and complex boxes; simple but satisfying pennants and much more... including a full theater for performances by paper dolls.

## math into art, hypnotizing and kaledscopic

## PORCELAINia

## Ancient Greek Geometry: The Game

The regular polygons have been kidnapped by ninjas. Are you a bad enough dude/tte to construct the regular polygons with nothing but a virtual compass and straightedge? [more inside]

## The architecture of bees: a study of hexagonal honey combs

People have long been interested in the architectural endeavors of animals. The internal structure of bee hives, the hexagonal combs of wax, have been amongst these ponderings, going back to Marcus Terentius Varro's

*Rerum Rusticarum Libri Tres*, a volume on Roman farm management. He wrote, "The geometricians prove that this hexagon inscribed in a circular figure encloses the greatest amount of space," and over the years, mathematicians have studied the hexagonal structures made by bees, and in 1998, Thomas Hales produced a mathematical proof for the classical hexagonal honeycomb conjecture, which "asserts that the most efficient partition of the plane into equal areas is the regular hexagonal tiling." [more inside]## Triple Gear

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear, three linked gears in space that can rotate together. A short writeup of the topology and geometry behind the triple gear on the arXiv.

## Healing Kaleidoscope

Emma Kunz was a telepathic healer and researcher. Even though she didn't consider herself an artist, the hypnotic symmetry found in her hand-drawn healing charts is breathtaking.

## Leonardo Interactivo

The Royal Spanish Library has put online today an interactive version of Leonardo da Vinci's Madrid Codices I & II. There are transcriptions of the text (in Spanish and Italian, click "T" on the bottom menu), animations of many of the mechanical contraptions (click play button "ver animacion") and the "Indice" in the bottom menu organizes the folios by theme.

## And collapsible hexagons are, I suppose, cool enough to at least amuse you a little bit during your class...

## William Thurston

"The real satisfaction from mathematics is in learning from others and sharing with others." William Thurston, one of the greatest mathematicians of the 20th century, has died. He revolutionized topology and geometry, insisting always that geometric intuition and understanding played just as important a role in mathematical discovery as did the austere formalism championed by the school of Grothendieck. Thurston's views on the relation between mathematical understanding and formal proof are summed up in his essay "On Proof and Progress in Mathematics." [more inside]

## Polygonal Portraiture

## Shapes of CSS

A large selection geometric shapes, all created with just one HTML element & CSS. An interesting take on geometry. Includes Space Invader. [more inside]

## Conformal Models of Hyperbolic Geometry

## Geometric Snow

## Morpion Solitaire

Morpion Solitaire is a very simple pencil-and-paper, line-drawing game for which the best possible score is not known! New records are still being set.

## Wheels within wheels

The best known packings of equal circles within a circle. Best packings with 1-12 circles. Best packings with 49-60 circles. Best packings with 1093-1104 circles. Also, circles whose areas form a harmonic series. Circles in an isosceles right triangle. Or generate your own circle packings. (Background for beginners: circle packing. Background for experts: circle packing.)

## The mathematical sculptures of Henry Segerman

Henry Segerman creates mathematical sculptures using 3D printing:
Round Möbius Strip,
Hopf Fibration,
Half of a 120-cell,
Rectified Tesseract,
Tesseract and 16-cell,
Hilbert Curve,
Knotted Cogs,
Round Klein Bottle [more inside]

## Growing a hyperdodecahedron

This short computer graphics animation

*presents the regular 120-cell: a four dimensional polytope composed of 120 dodecahedra and also known as the hyperdodecahedron or hecatonicosachoron.*[more inside]## Snowdecahedron

Snowdecahedron. When life hands you a blizzard, make a Platonic solid. "Temporary public art" from Dan Sternof Beyer.

## Never tell me the odds.

Measure-theoretic probability: Why it should be learnt and how to get started. The clickable chart of distribution relationships. Just two of the interesting and informative probability resources I've learned about, along with countless other tidbits of information, from statistician John D. Cook's blog and his probability fact-of-the-day Twitter feed ProbFact. John also has daily tip and fact Twitter feeds for Windows keyboard shortcuts, regular expressions, TeX and LaTeX, algebra and number theory, topology and geometry, real and complex analysis, and beginning tomorrow, computer science and statistics.

## Explorations of a Recreational Mathematician

Let's say you're me and you're in math class, and you're supposed to be learning about factoring. Trouble is, your teacher is too busy trying to convince you that factoring is a useful skill for the average person to know with real-world applications ranging from passing your state exams all the way to getting a higher SAT score and unfortunately does not have the time to show you why factoring is actually interesting. It's perfectly reasonable for you to get bored in this situation. So like any reasonable person, you start doodling.[more inside]

## Geometry, Surfaces, Curves, Polyhedra

Geometry, Surfaces, Curves, Polyhedra (many of which are beautiful) l Google Earth Fractals l fractals and chaos. [more inside]

## Happy 115th, Mr Fuller!

When he was 32, his life seemed hopeless. He was bankrupt and without a job. He was grief stricken over the death of his first child and he had a wife and a newborn to support. Drinking heavily, he contemplated suicide. Instead, he decided decided that his life was not his to throw away: it belonged to the universe. Buckminster Fuller embarked on "an experiment to discover what the little, penniless, unknown individual might be able to do effectively on behalf of all humanity." If the architect, author, designer, inventor, and futurist Richard Buckminster "Bucky" Fuller were still alive, he would be 115 years old today. Though he died in 1983, his legacy grows on through recordings of his ideas and the Buckminster Fuller Institute. [more inside]

## Topology on the Runway

There's always been hyperbole in fashion; but fashion became truly hyperbolic this week when mathematican William Thurston, winner of a 1982 Fields Medal for his revolutionary re-envisioning of low-dimensional topology and geometry, teamed up with designer Dai Fujiwara (of the house of Issey Miyake) to produce a Paris runway show based on the fundamental geometries of 3-dimensional spaces. Thurston and Fujiwara briefly interviewed. Thurston's famous essay "Proof and Progress in Mathematics" concerns, among other things, Thurston's belief that the production of mathematical understanding can be carried out by means other than the writing down of formal proofs (though fashion shows are not specifically mentioned.) Previously in wearable non-Euclidean geometry: Daina Taimina's hyperbolic skirt.

## Raise Thumb. Close One Eye. Squint.

The eyeballing game: compare your best attempts at several instinctive everyday tasks - determining a point of convergence, bisecting an angle, finding the midpoint of a line - against mathematical certainty. In a more financial mood? Play Chartgame: given a random historical stock chart of an unnamed S&P 500 company, choose to buy and sell as time advances to see if you can beat the market.

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