math-shirt

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One of the most intriguing aspects of mathematics is the connectivity between its branches. A great example is the topological proof of the Fundamental Theorem of Algebra.

The Fundamental Theorem of Algebra states that any nonconstant polynomial has a root in the complex plane. In fact, a degree n polynomial has n roots, if you count roots with multiplicity, but it suffices to show that there is at least one root. The Fundamental Theorem of Algebra was proved by Gauss in his doctoral dissertation.

To prove this using topology, we need the idea of the winding number of an oriented curve in the plane about the origin. (more…)

schrodingers-lolcat

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One of the fundamental scientific achievements of the 20th century was the development of quantum mechanics, which describes the behavior of small objects such as subatomic particles. Small objects don’t behave like billiard balls. We are still trying to understand all of the implications.

Reconciling the quantum mechanical behavior of subatomic particles with the ordinary behavior of macroscopic systems is still difficult, and this is the point of the thought experiment known as Schrodinger’s cat.

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geek-onesieObject oriented programming is one of the key advancements in computer programming in the past few decades. Describing systems as objects with properties and methods which interact with each other allows programmers to think about problems naturally and to reuse code libraries much more efficiently than in less powerful computing models. Object oriented programming allows individual, less experienced programmers to take advantage of frameworks and software development kits developed by teams of specialized professionals, lowering the time and experience needed to create polished, functional applications. Even as computers and operating systems become more complicated, object oriented programming leaves more time for programmers to have a life/family.

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math-shirt

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At first glance, the shirt on the left looks like a soccer jock shirt – but it’s actually a very nerdy math shirt.

A soccer ball (European football) usually has 12 pentagons and 20 hexagons, arranged in a highly symmetric fashion. The polyhedron most closely resembling this familiar object is the truncated icosahedron, an Archimedean solid.

Archimedean solids are an extension of the Platonic (regular) solids. Archimedean solids have regular polygons as faces, and have symmetries which send any vertex to any other. The rotational symmetries of the truncated icosahedron are the same as those for an icosahedron or dodecahedron. There are 60 rotational symmetries, isomorphic to the alternating group A5.

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