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Algorithms for finding prime numbers date back at least as far as ancient Greece, where mathematicians used a straightforward approach known as the Sieve of Erastothenes. The Sieve of Erastothenes works as follows: To find all the primes less than n, begin by writing down all the numbers from 1 to n in sequence. Then…
"If video games had been around in 350 BC, Euclid would have made a video game," Devlin told me. The thirteen books of Euclid's Elements would have been the supplemental material, a PDF file that you could read if you wanted to. "People think I'm joking—I absolutely mean that. Euclid would not have written a textbook…
Buzz. An example of a low-stress, win-win game is Prime Number Buzz. Students stand in a circle or at their desks and go around the room in order, saying either the next sequential number if it is a composite or “buzz” if it is a prime. If they are incorrect, they sit down, but they keep listening and when they catch…
Stanislas Dehaene brings up the Ramanujan-G.H.Hardy anecdote concerning the number 1729. The idea of running through the cubes of all integers from 1 to 12 in order to arrive at Ramanujan's spontaneous recognition of 1729 as the smallest positive integer that can be written in two distinct ways as the sum of two…
During a median follow-up of 20.7 years (interquartile range, 18.1-22.6 years), 190 SCDs, 281 fatal CHDs, 407 fatal CVDs, and 929 all-cause mortality events occurred. A total of 601, 1513, and 201 participants reported having a sauna bathing session 1 time per week, 2 to 3 times per week, and 4 to 7 times per week…
The theory is that numbers are self-organized around the smallest, most highly composite number, 12. The number 12 and many of its multiples (24, 36, 48, 60, etc.) are HCNs: highly composite numbers (with lots of divisors), which are extremely useful for measuring and proportions. Why are there 12 eggs in a carton, 12…
Occasionally he made a comment similar to Archimedes' "Eureka!" about a discovery, as he did when he wrong T T T=N. This is part of number theory, the field that Gauss called the Queen of Mathematics. A triangular number T is a number that you can get by adding up a string of consecutive whole numbers beginning with…
Theorem: There are infinitely many prime numbers. Proof: Suppose, contrary to the theorem, that there is only a finite number of primes. Thus, there will be a largest which we can call p. Now define a number n as 1 plus the product of all the primes: n = (2 X 3 X 5 X 7 X 11 X...X p) 1 Is n itself prime or composite?…
An effective strategy of predator satiation involves two adaptations. First, the synchrony of emergence or reproductions must be very precise, thus assuring that hte market is truly flooded, and only for a short time. Secondly, this flooding cannot occur very often, lest predators simply adjust their own life cycle to…
Let me tell you how at one time the famous mathematician Euclid became a physician. It was during a vacation, which I spent in Prague as I most always did, when I was attacked by an illness never before experienced, which manifested itself in chilliness and painful weariness of the whole body. In order to ease my…
230(231-1) ... is the greatest perfect number known at present, and probably the greatest that ever will be discovered; for; as they are merely curious without being useful, it is not likely that any person will attempt to find a number beyond it.
Mathematicians use the idea of proof to make a distinction between a 'conjecture' and a 'theorem', which bears a superficial resemblance to the OED's distinction between the two senses of 'theory'. A conjecture is a proposition that looks true but has never been proved. It will become a theorem when it has been…
He was 40 yeares old before he looked on geometry; which happened accidentally. Being in a gentleman's library, Euclid's Elements lay open, and 'twas the 47 El. libri I. He read the proposition. 'By G—,' sayd he, (He would now and then sweare, by way of emphasis) 'By G—,' sayd he, 'this is impossible!' So he reads the…