2015

SUnknownHypertwist: 2-sided Möbius strips and mirror universes

Fri, Dec 30, 2016

A Möbius strip is is a three dimensional object such as a ribbon with a single twist with its ends attached together. If you travel its length you will find that you return back were you started so it has a single side. So how do you create a Möbius strip with two sides. That gets interesting because you have to be in the right kind of universe.

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SUnknownFermat's Huge little theorem, pseudoprimes and Futurama

Fri, Oct 26, 2018

For a mathematician of Fermat's stature even his minor theorems are significant. Here Burkard applies Fermat's little theorem to tackle some intractable problems.

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SUnknownWhy don't they Teach this Simple Visual Solution? (Lill's method)

Thu, Apr 25, 2019

To find the solutions of a polynomial you just factor it, right? But not so easy when the exponents get large. Burkard shares several graphical methods that eliminate any guess work and, despite appearances, are equivalent to one another including an origami technique.

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SUnknownSecret of row 10: a new visual key to ancient Pascalian puzzles

Fri, Nov 29, 2019

Mathologer explores at a three color game that is equivalent to a modulus three addition game. The game is closely related to Pascal's Triangle with a symmetry alteration. It also produces fractals, the Sierpinski Triangle, which become obvious if you look at a large enough collection. The game can be reduced to binary addition or expanded to more colors and dimensions.

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SUnknownWhy Did They Prove this Amazing Theorem in 200 Different Ways? Quadratic Reciprocity Masterclass

Wed, May 13, 2020

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SUnknownHow Did Ramanujan Solve the Strand Puzzle?

Fri, Sep 04, 2020

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SUnknownThe Moessner Miracle. Why wasn't this discovered for over 2000 years?

Fri, Jul 16, 2021

It was known from the time of Pythagorus that adding up the odd numbers generates the square numbers. In 1951 Alfred Moessner finally took this process further using a similar sieve style algorithm that generates the cube and higher power numbers. But Burkard can't leave it at that and delves into the work of Karl Post who demonstrated the inputs and outputs mirror the relationships between addition and multiplication, multiplication and raising to a power, factorials and Pascal numbers.

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SUnknownThe Iron Man hyperspace formula really works (hypercube visualising, Euler's n-D polyhedron formula)

Fri, Aug 27, 2021

The powers of x + 2 have an interesting relationship to polyhedra. Let the power be the number of dimensions of the analog of a square; e.g 2 = square, 3 = cube, etc. Then the coefficients in the expanded polynomial equation provide the number of vertices, edges, faces, cells, etc of the square analog.

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