Repeating Decimals (Not a problem or a puzzle; just an amusement.) 1/1 1.0 1/2 = 0.5 1/3 = 0.[3] 1/4 = 0.25 1/5 = 0.2 1/6 = 0.1[6] 1/7 = 0.[142857] 1/8 = 0.125 1/9 = 0.[1] 1/10 = 0.1 1/11 = 0.[09] 1/12 = 0.08[3] 1/13 = 0.[076923] 1/14 = 0.0[714285] 1/15 = 0.0[6] 1/16 = 0.0625 1/17 = 0.[0.0588235294117647] 1/18 = 0.0[5] 1/19 = 0. [052631578947368421] 1/20 = 0.05 But after doing all this work I then googled......

My "Interesting Math Calculations" archive pages: http://www.j-bradford-delong.net/movable_type/archives/cat_math_calculations.html http://www.j-bradford-delong.net/cgi-bin/wiki.cgi?OneHundredInterestingMathCalculations...

One Hundred Interesting Mathematical Calculations Calculations and Puzzles, Number 11: The All-Knowing Alien Paradox An all-knowing alien who has a perfect computer model of your mind lands on earth. Xhsbr (that's a pronoun, not a proper name) shows you a box with two compartments, one compartment of which is clear and the other compartment of which is opaque. Each side has a door. You can see $10 in the clear part of the box. The alien says that xhsbr has...

One Hundred Interesting Mathematical Calculations Calculations and Puzzles, Number 10: The Grass Is Greener Paradox Someone standing behind a table shows you two envelopes. She tells you that one has twice as much cash in it as the other. She tells you to pick one and open it. You do. You discover that it has, say, $50 in it. She then asks you if you want to switch. You reason as follows. Either the two envelopes had $25 and $50...

One Hundred Interesting Mathematical Calculations, Number 9: False Positives Suppose that we have a test for a disease that is 98% accurate: if one has the disease, the test comes back "yes" 98% of the time (and "no" 2% of the time), and if one does not have the disease, the test comes back "no" 98% of the time (and "yes" 2% of the time). Suppose further that 0.5% of people--one out of every two hundred--actually has the disease. Your...

One Hundred Interesting Mathematical Calculations, Number 8: The Birthday Fact Look at the person next to you. What's the chance that your birthday and his are different? You would say it is about 364/365--only one time in 365 would your birthday turn out to be the same as hers. Now add a third person. What's the chance that your two birthdays are different, and that his birthday is different from both of yours? Well, the probability that your two...

One Hundred Interesting Mathematical Calculations, Number 7: Julius Caesar's Last Breath What's the chance that the breath you just inhaled contains at least one air molecule that was in Julius Caesar's last breath--the one in which he said (according to Shakespeare) "Et tu Brute? Then die Caesar"? Assume that the more than two thousand years that have passed have been enough time for all the molecules in Caesar's last breath to mix evenly in the atmosphere, and that only a...

One Hundred Interesting Mathematical Calculations, Number 6: How Much Blood Is There in the World? Begin with the fact that there are six billion people in the world, each of whom has about a gallon of blood. A gallon is about 0.133 cubic feet. So multiply 6 x 109 x 0.133 = 8 x 108 cubic feet of blood. How much blood is this? The cube root of 8 x 108 is 928. All the human blood in the world...

My kids--both The-Nine-Year-Old and The-Twelve-Year-Old--get the payoff from reading immediately. But they don't immediately get the payoff from math. I'm going to have to convince them that the payoff from math is there and is interesting, or else I'll have failed as a parent, and their future opportunities will be much smaller than they might have been. So now I'm getting ready to begin this task. I'll start for real over Christmas vacation... My User-Editable Interesting Math Calculations Page....

One Hundred Interesting Mathematical Calculations, Number 5: Exponential Growth and Human Populations We know from the experience of the colonization of North America that a reasonably well-fed human population with abundant land to hunt, fish, herd, and farm will double every quarter-century or so, even under pre-industrial disease and public health conditions, as long as it has not yet begun to go through the "demographic transition" that reduces birth rates to close to two children per potential mother. Suppose that...

One Hundred Interesting Mathematical Calculations, Number 4: Economic Growth Over the Past 500 Years Suppose that Virginia Postrel is an average contemporary American, with daily economic resources to spend of $100 or so, and that she can buy a five-pound bag of flour containing 7500 calories for $0.69. What fraction of her daily economic resources does she have to spend in order to obtain one calorie? This calculation is simple. If $0.69 gets her 7500 calories, then $0.69/7500 = 9.2...

One Hundred Interesting Mathematical Calculations, Number 3: The Strength of Gravity Newton's law of gravitation says that the gravitational force F exerted on one object (call it m1) by another object (call it m2) is given by the equation: F = Gm1m2/(d2) The force is equal to the gravitational constant G multiplied by the product of the two objects' masses and then divided by the square of the distance between the two objects. When we measure distances in meters and...

One Hundred Interesting Mathematical Calculations, Number Two: The Drake Equation: Cribbed from Wikipedia, the free encyclopedia. The Drake equation (also known as the Green Bank equation) is a famous result in the speculative fields of xenobiology and the search for extraterrestrial intelligence. This equation was devised by Dr. Frank Drake in the 1960s in an attempt to estimate the number of extraterrestrial civilizations in our galaxy with which we might come in contact. It seems to suggest that contact with...

One Hundred Interesting Mathematical Calculations, Number 1 Returning From World War II Bombing Missions: Suppose that you are a bomber pilot flying a B-17 in the European Theater of Operations during World War II. You know that 4% of bombers get shot down on average on each mission. You want to calculate the chance that you would successfully fly all the missions of your tour of duty--to make things simple, let's say 50 (a larger number than was actually asked...