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

Continue reading...# analysis

## Sliding Chords

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

Continue reading...## 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...

Continue reading...## 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...

Continue reading...## Koch Snowflake

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

Continue reading...## Reuleaux Wheel

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

Continue reading...## Thinned-Out Harmonic Series

You’re probably already aware that the harmonic series, which is the sum of the reciprocals of all natural numbers, diverges. In...

Continue reading...## Kakeya Needle Problem

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

Continue reading...## Cantor Set

Start with the interval [0,1]. Remove the (open) middle third of it, i.e. get (1/3, 2/3). Now remove the middle...

Continue reading...## Surface Area of a Sphere

The area of a disk enclosed by a circle of radius R is Pi*R2. The formula for the circumference of a...

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