You know the formula for the area of a circle of radius R. It is Pi * R2. But what...
Continue reading...calculus
Spherical Bands
Take any sphere and slice it up by parallel knives 1 inch apart. The areas of the spherical bands between the cuts...
Continue reading...Zero to the Zero Power
It is commonly taught that any number to the zero power is 1, and zero to any power is 0....
Continue reading...Holey Beads
Take a bead 5 inches high, and bore a hole through it from north pole to south pole in such...
Continue reading...Right Double Cone
Take a solid cylinder of radius R and height 2R. Remove the right “double cone” which passes through the center...
Continue reading...Wallis’ Formula
Here’s a fun formula for Pi involving an infinite product, known as Wallis’ Formula: (Pi/2) = (2*2)(4*4)(6*6)/(1*3)(3*5)(5*7) It is somewhat surprising that...
Continue reading...Inchworm on a Rubber Rope
Imagine a rubber rope one meter long. An inchworm starts at one end and travels along the rope at 1...
Continue reading...Successive Differences of Powers
List the squares: 0, 1, 4, 9, 16, 25, 36, 49, … Then take their successive differences: 1, 3, 5,...
Continue reading...Suspended Rope Trick
What is the shape of a suspended rope? Is there some function that describes it? Answer: it’s the cosh curve!...
Continue reading...Calculus Limerick
Here’s a calculus limerick: Integral z-squared dz from 1 to the cube root of 3 times the cosine of three pi over 9 equals...
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