It turns out that folding a pizza slice lengthwise to improve its rigidity is a great example of the "Remarkable Theorem" by Gauss. Cliff Stoll explains. (more…)

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It turns out that folding a pizza slice lengthwise to improve its rigidity is a great example of the "Remarkable Theorem" by Gauss. Cliff Stoll explains. (more…)

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Exotic polyhedron purveyor Dice Lab's crowning randomizer is its monstrous, $12 120-sided die. (more…)

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Exotic polyhedron purveyor Dice Lab's crowning randomizer is its monstrous, $12 120-sided die. (more…)

]]>Over at the Root Simple website, Mr. Homegrown wrote about the fun he's been having learning how to draw Islamic geometric patterns from this book by Eric Broug.

]]>It’s a book of step by step drawing instructions. All you need is a ruler, compass, pencil and pen. While the geometry behind theses patterns is enormously sophisticated, actually drawing out the shapes is surprisingly easy and relaxing. It’s also a fun and painless lesson in geometry, especially for those of us not inclined towards math..

Over at the Root Simple website, Mr. Homegrown wrote about the fun he's been having learning how to draw Islamic geometric patterns from this book by Eric Broug.

]]>It’s a book of step by step drawing instructions. All you need is a ruler, compass, pencil and pen. While the geometry behind theses patterns is enormously sophisticated, actually drawing out the shapes is surprisingly easy and relaxing. It’s also a fun and painless lesson in geometry, especially for those of us not inclined towards math..

From 1966, René Jodoin's beautiful minimalist animation of a geometric ballet, "Notes on a Triangle." Jodoin, who died earlier this year, was founder of the National Film Board of Canada's animation studio. "Note on a Triangle" was only one of several films meant as an introduction to geometric forms. See more here.

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From 1966, René Jodoin's beautiful minimalist animation of a geometric ballet, "Notes on a Triangle." Jodoin, who died earlier this year, was founder of the National Film Board of Canada's animation studio. "Note on a Triangle" was only one of several films meant as an introduction to geometric forms. See more here.

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Tentacles made of cubes reach for you from within the watery abyss. "You're not supposed to be here," an unseen being informs you as you descend into the first level of the game *Euclidean*. Deep sea creatures made of shapes swarm, pulse and strain around you—and soon, they notice you. "Everything here will kill you," the voice intones a few moments later.
(more…)

Tentacles made of cubes reach for you from within the watery abyss. "You're not supposed to be here," an unseen being informs you as you descend into the first level of the game *Euclidean*. Deep sea creatures made of shapes swarm, pulse and strain around you—and soon, they notice you. "Everything here will kill you," the voice intones a few moments later.
(more…)

“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.” —Visualizing Math.
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“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.” —Visualizing Math.
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Designer Jessica Rosenkrantz writes, "I made this 3D printed dress and the MoMA just acquired it. This video, filmed at Shapeways factory showing the printing and depowdering of the dress (there's also this one, documenting the dress's sounds and movements). (more…)

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Designer Jessica Rosenkrantz writes, "I made this 3D printed dress and the MoMA just acquired it. This video, filmed at Shapeways factory showing the printing and depowdering of the dress (there's also this one, documenting the dress's sounds and movements). (more…)

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Vi Hart, the Internet's favorite manic vlogging mathematician, has released a new video in which she teams up with math artists Andrea Hawksley and Gwen Fisher, and Gwen's sister Ruth of Sweets by Ruth. The four of them bake satisfyingly precise and geometric gingerbread polygons, then build up a variety of astounding three dimensional forms by piecing them together with icing. The video is both hunger-inspiring and brain-inspiring, and is likely to be the best thing you watch this week.

Cookie Shapes
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Vi Hart, the Internet's favorite manic vlogging mathematician, has released a new video in which she teams up with math artists Andrea Hawksley and Gwen Fisher, and Gwen's sister Ruth of Sweets by Ruth. The four of them bake satisfyingly precise and geometric gingerbread polygons, then build up a variety of astounding three dimensional forms by piecing them together with icing. The video is both hunger-inspiring and brain-inspiring, and is likely to be the best thing you watch this week.

Cookie Shapes
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"Penrose Stars", a GIF created by davidope and inspired by the famed impossible object, the Penrose stairs. See more of dvdp's abstract GIFs here. *(via Imaginary Foundation)*]]>

"Penrose Stars", a GIF created by davidope and inspired by the famed impossible object, the Penrose stairs. See more of dvdp's abstract GIFs here. *(via Imaginary Foundation)*]]>

Fdecomite has revisited his tessellated Escher cookie-cutters, with a new set of cutters and some new baking that he's posted to the Boing Boing Flickr pool.

Yet another set of Escher cookie cutters
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Fdecomite has revisited his tessellated Escher cookie-cutters, with a new set of cutters and some new baking that he's posted to the Boing Boing Flickr pool.

Yet another set of Escher cookie cutters
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In the Boing Boing Flickr Pool the fractal-obsessed Fdecomite posts the latest iteration in a series of experiments with tessellated, Escher cookie-cutters. Bake-time expansion creates irregularities that lead to a chewy (literally) series of interlock-imperfections, which give old MC's classic a bio-organic air that rather invigorates it.

You can 3D print interlocking lizard cutters with a free model from Thingiverse. Fdecomite, if you're reading this, please post in the comments with a link to the cookie cutters you used here!

**Update:** From the comments, Fdecomite writes, "Hi, those are cookie cutters I made from aluminium foil.I also made some 3D printed Escher cookie cutters you can find in my Shapeways shop.

Escher Cookie Cutters - The Sequel
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In the Boing Boing Flickr Pool the fractal-obsessed Fdecomite posts the latest iteration in a series of experiments with tessellated, Escher cookie-cutters. Bake-time expansion creates irregularities that lead to a chewy (literally) series of interlock-imperfections, which give old MC's classic a bio-organic air that rather invigorates it.

You can 3D print interlocking lizard cutters with a free model from Thingiverse. Fdecomite, if you're reading this, please post in the comments with a link to the cookie cutters you used here!

**Update:** From the comments, Fdecomite writes, "Hi, those are cookie cutters I made from aluminium foil.I also made some 3D printed Escher cookie cutters you can find in my Shapeways shop.

Escher Cookie Cutters - The Sequel
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Here's glassblower Alan Bennett's astounding triple-nested Klein bottle, a beautiful thing:

A single surface model made by Alan Bennett in Bedford, United Kingdom. It consists of three Klein bottles set inside each other to produce, when cut, three pairs of single-twist Mobius strips. A Klein bottle has no edges, no outside or inside and cannot be properly constructed in three dimensions.

Klein bottle, 1995.
(*via Neatorama*)

(*Image: Science Museum/Science & Society Picture Library*)
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Here's glassblower Alan Bennett's astounding triple-nested Klein bottle, a beautiful thing:

A single surface model made by Alan Bennett in Bedford, United Kingdom. It consists of three Klein bottles set inside each other to produce, when cut, three pairs of single-twist Mobius strips. A Klein bottle has no edges, no outside or inside and cannot be properly constructed in three dimensions.

Klein bottle, 1995.
(*via Neatorama*)

(*Image: Science Museum/Science & Society Picture Library*)
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Duann from Shapeways sez, "Infinite bacon is now possible direct from Shapeways 3D printers. The dream of 3D printing food, infinite possibilities, infinite supply is now possible with the ultimate food to infinity, 3D printed Bacon Mobius Strip. Finally it is possible, infinite 3D printed bacon with the Bacon Mobius Strip that is not delicious but also vegan and kosher friendly."

3D Printing Bacon to Infinity (VIDEO)
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Duann from Shapeways sez, "Infinite bacon is now possible direct from Shapeways 3D printers. The dream of 3D printing food, infinite possibilities, infinite supply is now possible with the ultimate food to infinity, 3D printed Bacon Mobius Strip. Finally it is possible, infinite 3D printed bacon with the Bacon Mobius Strip that is not delicious but also vegan and kosher friendly."

3D Printing Bacon to Infinity (VIDEO)
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The incomparably great Vihart continues her Doodling in Math Class video series with a history and demonstration of the miraculous Hexaflexagon, a simple-to-fold paper hexagon that contains several iterations of itself, which can be found by turning it inside-out over and over again. Sure to delight, inform, entertain, and mystify!

Historical Note: This video is based on a true story. Arthur H. Stone really did invent the hexaflexagon after playing with the paper strips he'd cut off his too-wide British paper, and really did start a flexagon committee (which we'll hear more about in the next video). The details and dialogue, however, are my own invention.

Hexaflexagons
(*Thanks, Fipi Lele!*)
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The incomparably great Vihart continues her Doodling in Math Class video series with a history and demonstration of the miraculous Hexaflexagon, a simple-to-fold paper hexagon that contains several iterations of itself, which can be found by turning it inside-out over and over again. Sure to delight, inform, entertain, and mystify!

Historical Note: This video is based on a true story. Arthur H. Stone really did invent the hexaflexagon after playing with the paper strips he'd cut off his too-wide British paper, and really did start a flexagon committee (which we'll hear more about in the next video). The details and dialogue, however, are my own invention.

Hexaflexagons
(*Thanks, Fipi Lele!*)
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