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**Weekly 7: Fractals**

In class we did an overview of fractals, learning about Julia sets, the Mandelbrot set, and Sierpinski's Carpet. What these have in common is their repetitive nature: at every magnification, these sets have a repeating pattern that is a scaled copy of the o...

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**Last Daily: Course Reflection**

My favorite aspect of the course was going through the history of mathematics, and learning about the people who were behind many of the subject's major milestones. Doing this seemed to give math a more "personal" feel, whereas in other courses we simply le...

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**Journey Through Genius**

The book I read and reviewed earlier this semester was The Mathematical Universe , by William Dunham. His book Journey Through Genius seemed like it would be similar in style and content, so I thought I'd check it out for my second book. One thing I immedi...

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**Daily 13: Mathematical Paradoxes**

Aristotle's Wheel Aristotle's Wheel is a paradox found in the Mechanica and consists of two wheels, one within another, that roll along a surface. It is constructed so, like in the image below, two horizontal lines trace the bottom of the circle and appea...

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**Daily 12 and Weekly 6: Gauss and Minorities in Mathematics**

Gauss proved a conjecture first proposed by Fermat, which stated that any natural number can be expressed as the sum of three triangular numbers. In order to fully understand this, we must first make sure we know what triangular numbers are. From wikipedia...

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**Daily 10 and Weekly 5: The Mathematical Universe**

I contained my daily and weekly assignment in one document, whose length got a bit out of hand. Sorry about that. Here it is.

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**Fermat's Last Theorem**

I watched the video suggested on the course page for my daily work, which provided an overview of proving Fermat's Last Theorem. It's interesting that it took so long to prove a theorem that seems so simple compared to other theorems we have encountered. ...

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**Daily 8 and Weekly 4: Fibonacci**

Fibonacci (History of Math, compiled using Wikipedia articles and handouts from class.) Leonardo Pisano Bigollo, more popularly known as Fibonacci, was an Italian mathematician born circa 1170. His most famous work, Liber Abaci (no, not Liberace ), was on...

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**Daily 7: A Few Fibonacci Propositions**

After hunting around the internet, I came across several propositions made by Fibonacci and theorems regarding the Fibonacci sequence. Here are proofs of a couple of the things I came across. (Knowledge of HTML coding is lacking, so some of the equations lo...

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**Daily 6 and Weekly 3: Cube from Class and a Miscellany of Mathematics**

In class, we were to build a cube that is broken into three parts: one part that consists of half the volume of the cube, another that is one third the volume of the cube, and a final piece that is one sixth the volume of the cube. I began with a drawing of...

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