If you liked the Fun Fact Multiplication by 11, you’ll enjoy seeing how to take that idea one step farther. Here’s...

Continue reading...# algebra

## Squaring Quickly

You may have seen the Fun Fact on squares ending in 5; Here’s a trick that can help you square ANY...

Continue reading...## Multidimensional Newton’s Method

You’ve probably heard of Newton’s Method from your calculus course. It can be used to locate zeros of real-valued functions. But did...

Continue reading...## Volume of a Ball in N Dimensions

The unit ball in Rn is defined as the set of points (x1,…,xn) such that x12 + … + xn2 <= 1. What...

Continue reading...## Really Complex Matrices

If you know how to multiply 2×2 matrices, and know about complex numbers, then you’ll enjoy this connection. Any complex number...

Continue reading...## Taylor-made Pi

After learning about the Taylor series for 1/(1+x) in calculus, you can find an interesting expression for Pi very easily. Start with...

Continue reading...## Banach-Tarski Paradox

Did you know that it is possible to cut a solid ball into 5 pieces, and by re-assembling them, using...

Continue reading...## Sierpinski-Mazurkiewicz Paradox

If you’ve seen the Banach-Tarski paradox, you know that it is possible to cut a solid 3-dimensional ball into 5 pieces...

Continue reading...## Descartes’ Rule of Signs

Given a polynomial such as: x4 + 7×3 – 4×2 – x – 7 it is possible to say anything about how many positive real...

Continue reading...## Fundamental Group

You are abducted by space aliens and dumped, blindfolded, on a strange asteroid! Removing your blindfold, you decide to play...

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