Mathematician and origami expert Tom Hull created this pleated multi-sliced cone from paper, never before accomplished since Robert Lang designed it via computer.

Origami Kids has both the pattern and the final result, which Hull recommends attempting with high-quality origami paper.

Hull is highly regarded in the fields of math and origami for creating PHIZZ unit (pentagon-hexagon zig-zag).

Here's a simple PHIZZ shape by Flickr user fdecomite:

And a pretty PHIZZ tunnel by Flickr user lhuerta:

]]>
*(Via Pickover)*]]>

The thinking behind Citizen Maths comes from a group of maths-education researchers at the Institute of Education in London.

]]>Seb writes, "Citizen Maths is a new CC-BY licensed open online maths course produced in the UK for adults and college students who want to improve their grasp of maths at what in the UK is known as Level 2 (the level that 16 year old school leavers are expected to reach, though many do not)."

The thinking behind Citizen Maths comes from a group of maths-education researchers at the Institute of Education in London. The content being released with the first run of Citizen Maths focuses on one powerful idea in mathematics, that of proportion which sits behind so many aspects of every-day maths, for example sharing out costs, or altering a mixture, comparing amounts, or scaling something up or down.

Citizen Maths includes a series of short instructional videos by two experienced â€œto-cameraâ€ maths teachers, aiming to give learners the feeling that they are in a one-to-one tutorial with a skilled teacher.

The course makes extensive use of applets that offer an on-screen manifestation of the mathematical concepts involved, intended to help learners see the mathematical idea in a concrete way, prior to working in more detail on the computational aspects of the idea.

Citizen Maths
(*Thanks, Seb!*)
]]>

Regular BB readers know one of my favorite head trips is the idea that we're living in a simulation or control system of some kind. Decades before The Matrix, folks like Jacques Vallee, John Keel, Stephen Wolfram, Rudy Rucker, Hans Moravec, and Ed Fredkin explored this notion. And of course it's also been the subject of countless science fiction novels. In recent years, Oxford philosopher Nick Bostrom developed a mathematical argument to support the mind-bending theory. A week ago, UC Berkeley mathematician Edward Frankel, author of Love and Math: The Heart of Hidden Reality, summed up the Simulation Argument in the New York Times Sunday Review and asked whether we can test the hypothesis.

Is the Universe a Simulation? *(Thanks, Marina Gorbis!)*]]>
*The Simpsons *is arguably the most successful television show in history. Inevitably, its global appeal and enduring popularity have prompted academics (who tend to overanalyze everything) to identify the subtext of the series and to ask some profound questions.

One group of intellectuals authored a text arguing that *The Simpsons *essentially provides viewers with a weekly philosophy lecture. *The Simpsons and Philosophy*, edited by William Irwin, Mark T. Conard, and Aeon J. Skoble, claims to identify clear links between variousepisodes and the issues raised by history's great thinkers, includingAristotle, Sartre, and Kant. Chapters include "Marge's Moral Motivation," "The Moral World of the Simpson Family: A Kantian Perspective,"and "Thus Spake Bart: On Nietzsche and the Virtues of BeingBad."

By contrast, Mark I. Pinsky's *The Gospel According to The Simpsons* focuses on the spiritual significanceof *The Simpsons*. This is surprising, because many charactersappear to be unsympathetic toward the tenets of religion. Regularviewers will be aware that Homer consistently resists pressure to attendchurch each Sunday, as demonstrated in "Homer the Heretic"(1992): "What's the big deal about going to some building every Sunday?I mean, isn't God everywhere? . . . And what if we've picked the wrong religion? Every week we're just making God madder and madder?"

Even President George H. W. Bush claimed to have exposed the real message behind *The Simpsons*. He believed that the series was designed to display the worst social values. This motivated the most memorable sound bite from his speech at the 1992 Republican National Convention, which was a major part of his re-election campaign: "We are going to keep on trying to strengthen the American family to make American families a lot more like the Waltons and a lot less like the Simpsons."

The writers of *The Simpsons *responded a few days later. The next episode to air was a rerun of "Stark Raving Dad" (1991), except the opening had been edited to include an additional scene showing the family watching President Bush as he delivers his speech about the Waltons and the Simpsons. Homer is too stunned to speak, but Bart takes on the president: "Hey, we're just like the Waltons. We're praying for an end to the Depression, too."

However, all these philosophers, theologians, and politicians have missed the primary subtext of the world's favorite TV series. The truth is that many of the writers of *The Simpsons *are deeply in love with numbers, and their ultimate desire is to drip-feed morsels of mathematics into the subconscious minds of viewers. In other words, for more than two decades we have been tricked into watching an animated introduction to everything from calculus to geometry, from pi to game theory, and from infinitesimals to infinity.

"Homer 3," the third segment in the three-part episode "Treehouse of Horror VI" (1995) demonstrates the level of mathematics that appears in *The Simpsons*. In one sequence alone, there is a tribute to history's most elegant equation, a joke that only works if you know about Fermat's last theorem, and a reference to a $1 million mathematics problem. All of this is embedded within a narrative that explores the complexities of higher-dimensional geometry.

"Homer 3" was written by David S. Cohen, who has an undergraduate degree in physics and a master's degree in computer science. These are very impressive qualifications, particularly for someone working in the television industry, but many of Cohen's colleagues on the writing team of *The Simpsons *have equally remarkable backgrounds in mathematical subjects. In fact, some have PhDs and have even held senior research positions in academia and industry. Here is a list of degrees for five of the nerdiest writers:

**J. Stewart Burns **

BS Mathematics, Harvard University MS Mathematics, UC Berkeley

**David S. Cohen **

BS Physics, Harvard University

MS Computer Science, UC Berkeley

**Al Jean **

BS Mathematics, Harvard University

**Ken Keeler **

BS Applied Mathematics, Harvard University

PhD Applied Mathematics, Harvard University

**Jeff Westbrook **

BS Physics, Harvard University

PhD Computer Science, Princeton University

In 1999, some of these writers helped create a sister series titled *Futurama*, which is set one thousand years in the future. Not surprisingly, this science fiction scenario has allowed them to explore mathematical themes in even greater depth, with references to Moebius strips, Klein bottles, taxicab numbers and numerous nods to binary arithmetic.

If you remain dubious about my claim that *The Simpsons* and *Futurama* are essentially mathematical textbooks hidden within an animated sit-com format, then I will leave you with a brief description of one particular episode that should dispel any doubts.

A *Futurama* episode entitled "The Prisoner of Benda" (2010) has a storyline that includes a mind-switching machine that can transfer the mind of one person into the body of a second person, and vice versa. Various characters - including Fry, Bender, Leela, and Professor Farnsworth - indulge in an orgy of mind-switching, before they realise that two people who have switched minds cannot switch back. Hence, two people who have switched can only restore their minds via switches with third parties, who act as intermediate vessels for minds trying to find their rightful owners. This raises an interesting mathematical question; "How many intermediate people are required in order to guarantee that people can return to their own minds, regardless of the number of people and the number of previous switches?"

Ken Keeler, a *Futurama* writer who has a doctorate in applied mathematics, took up the challenge of investigating mind-switching and developed a proof which demonstrates that introducing two fresh people into any group, regardless of the group's mind-switching history, is sufficient to unmuddle all the minds. The full proof appears on a blackboard in one of the final scenes of the episode. Known as Keeler's theorem or the Futurama theorem, this curious and credible piece of mathematics has subsequently inspired other mathematicians to explore related mind-switching mysteries.

This proves that the writers behind *The Simpsons* and *Futurama* have a unique set of mathematical talents, as no other sitcom can boast the creation of a genuinely innovative and bespoke piece of mathematics. Indeed no other series in the history of primetime television has included so many mathematical references.

*This excerpt has been adapted from the introduction to The Simpsons and Their Mathematical Secrets by Simon Singh. Copyright (c) 2013 by Simon Singh. Used by permission of Bloomsbury USA*

In this video, Mariano Tomatis shows how to create chocolate out of nothing. Here is his explanation of this wonderful phenomenon, known as a missing square or vanishing area puzzle. *(Thanks, Ferdinando Buscema!)*]]>
*(3.14-pi.net)*

[π] is a lovely and simple page that "explores the musical rhythm within 100,000 digits of π, an irrational number. #1 = Day | #0 = Night | #2–9 = La Musica." [π] *(3.14-pi.net)*]]>

The Evil Mad Scientists were presented with a challenge: inscribe one of Cliff Stoll's hand-blown Klein bottles, an object of surpassing beauty and odd topology. They modified an Eggbot plotter to etch the surface of a Klein bottle with a diamond engraver attachment.

So how would you etch the curved surface of a Klein bottle? It turns out, to our surprise, that it is remarkably easy to do it with an Ostrich Eggbot fitted with a diamond engraver attachment.

There was one complication, which is that a Klein bottle is a funny shaped object! In order to fixture the Klein bottle in the Eggbot, we made a couple of extra large couplers—much larger than the tiny pads normally used to hold the ends of an egg—with EVA foam rubber pads on their surfaces. The extra large couplers held the Klein bottle securely for rotation.

Marking Klein Bottles with the Eggbot
]]>

The Cartoon Introduction to Statistics is a new book by Grady Klein and Alan Dabney that is a top-notch introductory grounding in statistical concepts told through a series of witty, funny cartoons that relate stats to everything from fish populations to alien opinion surveys. This is a

The authors do a great job of conveying the source material in clear, stepwise fashion, and made the wise decision to put the equations at the back of the book in an appendix called "The Math Cave." They don't delve deeply into any intermediate subjects like assessing correlation (for this, I highly recommend 1993's The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith, about which I can't say enough great and enthusiastic things), but that's probably a wise tactical decision. Confining the material to basics makes the whole work into an unqualified success.

The Cartoon Introduction to Statistics
]]>

Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
(*Thanks, Dad!*)

Here's a great video pondering the objective reality of mathematics, and running down all the different schools of thought on where mathematical truth comes from -- does it exist outside of systems of codification by intelligent beings, as an eternal part of the universe; or is it something that we invent through codification?

Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
(*Thanks, Dad!*)
]]>

Beast Academy is a set of grade three math textbooks and practice books structured as comic books about monsters. The books are "aligned to the common core state standards for grade three," if that matters to you. What's more significant is that they're actually really good math textbooks that introduce their subjects in a clear and easy-to-follow fashion, carefully linking each concept to the last; and the exercises are lively, fun, and built around stories that dovetail smoothly into puzzles, games, and other ways of putting the knowledge into practice. The monsters are great, too -- wonderful illustrations from Erich Owen, whose work you may recognize from the graphic novel adaptation of my story I, Robot.

]]>

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.

]]>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*)
]]>
*(thanks, Dean Putney!)*]]>*(thanks, Dean Putney!)*]]>