The conic sections are formed by taking flat slices of a solid double right cone. You can generate them with...
Continue reading...geometry
Pick’s Theorem
A lattice point in the plane is any point that has integer coordinates. Let P be a polygon in the plane whose vertices have...
Continue reading...How GPS Works
The intersection of two spheres is generally a circle (but might also be a point or the empty set). That...
Continue reading...Pizza Slices
Take a pizza and pick an arbitrary point in it. Suppose you cut the pizza into 8 slices by cutting...
Continue reading...Memorizing Pi
The digits of Pi are fascinating. As the ratio of the circumference of a circle to its diameter, Pi has...
Continue reading...Sum of Cubes
The sum of cubes is just the square of the triangular numbers! 13 + 23 + … + n3 = (1 + 2 + … + n)2. And there...
Continue reading...Reflecting on the Hyperbola
Most calculus students have learned of the “reflecting properties” of the parabola and the ellipse. If a “beam of light” emanates from the...
Continue reading...Bike with Square Wheels
Ride a bike with round wheels and it rolls smoothly on a flat road (i.e., the axle remains level). Can...
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