There’s a nice way to see why the formula for the area of a circle of radius R is: Pi...
Continue reading...calculus
Impossible Integral?
The following integral may be problematic for a freshman calculus student, even if armed with a list of antiderivatives: INTEGRAL0...
Continue reading...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...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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