The digits of Pi are fascinating. As the ratio of the circumference of a circle to its diameter, Pi has...
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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...
Continue reading...One Equals Zero!
The following is a “proof” that one equals zero. Consider two non-zero numbers x and y such that x =...
Continue reading...Proofs without Words
There are many facts which can be proved just by looking at a picture! For instance:x2 – y2 = (x+y) (x-y)is illustrated...
Continue reading...Pigeonhole Principle
Here’s a challenging problem with a surprisingly easy answer: can you show that for any 5 points placed on a sphere,...
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