There are lots of Pythagorean triples; triples of whole numbers which satisfy:x2 + y2 = z2. But are there any which satisfyxn + yn =...
Continue reading...geometry
Slices of Hanging Cubes
Hang a cube from one of its vertices. Now, if you slice it horizontally through its center, you get a...
Continue reading...Koch Tetrahedron
In Koch Snowflake we saw an interesting fractal snowflake-like object that is obtained when gluing smaller triangles iteratively to the sides of...
Continue reading...Hyperbolic Geometry
In the Fun Fact on Spherical Geometry, we saw an example of a space which is curved in such a way...
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...Sphere Eversions
If you take a loop of string in the plane and place an arrow along it pointing clockwise, is it...
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...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...
Continue reading...Chords of an Ellipse
Consider N equally spaced on points on the unit circle, with the point P=(1,0) as one of these equally spaced...
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...
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