# calculus

## Area of a Circle or Regular Polygon

There’s a nice way to see why the formula for the area of a circle of radius R is: Pi...

## Impossible Integral?

The following integral may be problematic for a freshman calculus student, even if armed with a list of antiderivatives: INTEGRAL0...

## Sliding Chords

Take a circle C, and a chord in the circle. Now slide the chord around the circle. As you do this, the...

## Tower of Powers

Consider an infinite “tower of powers” of x, defined by x^x^x^… = x^(x^(x^…)) Can we find a value of x...

## Rolling Polygons

Perhaps you’ve learned from a calculus class that as you roll a circular disk along a straight line, that the area under...

## Koch Snowflake

Snowflakes are amazing creations of nature. They seem to have intricate detail no matter how closely you look at them....

## Reuleaux Wheel

A Reuleaux Triangle is a plump triangle with rounded edges, formed in the following way: take the three points at the corners...

## Kakeya Needle Problem

What is the smallest-area convex set in the plane inside which a needle (unit straight line segment) can be reversed...