By Dominic Olivastro
Match wits with the good minds of the world’s maximum civilizations during this attention-grabbing number of historical conundrums, brainteasers, and mind-benders.
• What do prehistoric bone markings and sleek desktop technological know-how have in common?
• What is the secret of pi that stumped generations of old mathematicians?
• What are the traditional puzzle origins of renowned video games reminiscent of tic-tac-toe and chess?
• Can you resolve the puzzles posed to emperor Charlemagne by means of Alcuin of York?
• What’s the key lore at the back of magic squares that captured the mind's eye of chinese language emperors, Persian mystics, and Benjamin Franklin?
Dominic Olivastro offers a well-liked historical past of arithmetic by way of targeting the puzzles that civilizations posed for his or her personal schooling and leisure. listed below are vintage “puzzle difficulties” from historical Africa, Egypt, Persia, China, and Greece and from cultures and texts spanning the center a long time and the Renaissance all of the approach to the present.
every one puzzle is associated with insightful people and clinical heritage that is helping make clear the mysterious objective and starting place of the matter. attention-grabbing clues for knowing solutions draw on glossy problem-solving thoughts and result in historical secrets and techniques that, prior to now, have not often been understood. no matter if you decipher them for his or her historic value, classical knowledge, or simply for the sheer, maddening enjoyable of it, those pleasant puzzles offer a distinct, wonderful, and enlightening advisor to the evolution of the human brain.
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Extra resources for Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last Ten Centuries
A large figure on his left was called a harpedonaptai,or rope-stretcher, the government official who actually measured the farmer's land; one coil of rope has already been drawn taut, and another is still wrapped around his shoulder. The stretched rope is used as a primitive measuring tool to obtain the straight-line distance of one side of the field. Based on these figures Menna had to calculate the farmer's taxes. It is possible that the method of computation had been learned from the manuscript that Ahmes had copied.
The probability in question is found by dividing the two areas. The area of the circle-the area of any circle-is 7Tr 2, which in this case simply equals pi, since the radius was set at 1. The area of the square is 4. Therefore the probability in question is P = 7T/4. Again, this means pi = 4P. Theoretically, it should be possible to toss several coins onto the figure and keep track of the number that fall anywhere on the square (which we will call s) and the number of these that also fall on the circle (called c).
In fact, the three sons get 9, 6, and 2 camels respectively. There is exactly one camel left over, which is returned to the lawyer. The puzzle works because the sum of the fractions is itself a fraction of the form dl(d+ 1). Specifically, we get 1/2 + 1/3 + 1/9 = 17/18. Because the numerator and denominator differ by one, precisely one new camel must be added in order to effect the division. The character of an Arabian merchant as well as the use of camels points to a Middle East origin. This may also explain the fact that the fractions are unit fractions.
Ancient Puzzles: Classic Brainteasers and Other Timeless Mathematical Games of the Last Ten Centuries by Dominic Olivastro