The digits of Pi are fascinating. As the ratio of the circumference of a circle to its diameter, Pi has...
Continue reading...easy
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...
Continue reading...Multiplication by 11
Multiplication by 11 is easy! To multiply by a 2-digit number add the two digits and place the sum in...
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...Magic Squares, indeed!
Perhaps you’ve seen the magic square 8 1 6 3 5 7 4 9 2 which has the property that all rows,...
Continue reading...Leapfrog Addition
Here’s a nice mathematical magic trick based on properties of the Fibonacci sequence. Give your friend a card with ten blank lines, numbered 1...
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...Pascal’s Triangle
Consider the triangle in Figure 1, called Pascal’s triangle. It consists of numbers where each entry is the sum of the...
Continue reading...