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1729 — The First Taxicab NumberEpisode five of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Curious properties sometimes lurk within seemingly undistinguished numbers. 1729 sparked one of maths most famous anecdotes: a young Indian, Srinivasa Ramanujan, lay dying of TB in a London hospital. G.H. Hardy, the leading mathematician in England, visited him there. "I came over in cab number 1729," Hardy told Ramanujan. "That seems a rather dull number to me."
"Oh, no!" Ramanujan exclaimed. "1729 is the smallest number you can write as the sum of two cubes, in two different ways." Most of us would use a computer to figure out that 1³ + 12³ = 9³ + 10³ = 1729. Ramanujan did it from his sickbed without blinking.https://huffduffer.com/adactio/6898
https://huffduffer.com/adactio/6898
Sat, 8 Aug 2009 11:59:43 GMTmathematicsfive numbersbook:author=simon singhbbc1729ramanujan numberstaxicab numbers6.67 x 10^-11 – The Number That Defines the Universe.Episode four of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Newton’s equation of gravity included a number G, which indicates the strength of gravitation. It took 100 years before the shy Englishman Henry Cavendish (he left notes for his maids because he was too shy to talk to women) measured G to be 6.67 x 10^-11 Nm²/Kg². It allowed him to weigh the Earth itself. There has been an ever-greater desire to measure this number with accuracy, which even implied an antigravity at times. How did we measure this tiny number and what does it mean for the universe? The Astronomer Royal Martin Rees explains that a large value for G would mean that stars would burn too quickly and a low value would mean that the stars would not form in the first place, so is G perfectly tuned for life? Is God a mathematician?https://huffduffer.com/adactio/6873
https://huffduffer.com/adactio/6873
Thu, 6 Aug 2009 22:59:15 GMTmathematicsfive numbersbook:author=simon singhbbcgravitymartin reesgravitationscience6 Degrees of SeparationEpisode three of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Six is often treated as 2x3, but has many characteristics of its own. Six is also the "pivot" of its divisors (1+2+3=6=1x2x3) and also the centre of the first five even numbers: 2, 4, 6, 8, 10. Six seems to have a pivoting action both mathematically and socially. How is it that everyone in the world can be linked through just six social ties? As Simon discovers, the concept of “six degrees of separation” emerged from a huge postal experiment conducted by the social psychologist Stanley Milgram in 1967. Milgram asked volunteers to send a package by mail to one of a hundred people chosen at random. But they could only send mail to people they knew on first name terms.https://huffduffer.com/adactio/6846
https://huffduffer.com/adactio/6846
Wed, 5 Aug 2009 21:58:49 GMTmathematicsfive numbersbook:author=simon singhbbcsix degreessmall worldnetwork theorystanley milgramduncan watts2 — At The DoubleEpisode two of A Further Five Numbers, the BBC radio series presented by Simon Singh.
We all remember the story of the Persian who invented chess and who asked to be paid with 1 grain of rice on the first square, 2 on the second, 4 on the third and so on, doubling all the way to the 64th square. He bankrupted the state!
This doubling is a form of exponential growth, which appears in everything from population growth to financial inflation to the inflation theory that supposedly caused the Big Bang. https://huffduffer.com/adactio/6805
https://huffduffer.com/adactio/6805
Mon, 3 Aug 2009 23:46:09 GMTmathematicsfive numbersbook:author=simon singhbbctwoexponential growth1 — The Most Popular NumberEpisode one of A Further Five Numbers, the BBC radio series presented by Simon Singh.
Literally, the most popular number, as it appears more often than any other number. More specifically, the first digit of all numbers is a 1 about 30% of the time, whereas it is 9 just 4% of time. This was accidentally discovered by the engineer Frank Benford. It works for all numbers – mountain heights, river lengths, populations, etc.https://huffduffer.com/adactio/6736
https://huffduffer.com/adactio/6736
Thu, 30 Jul 2009 08:52:41 GMTmathematicsfive numbersbook:author=simon singhbbconebenford's lawGame TheoryEpisode five of Another Five Numbers, the BBC radio series presented by Simon Singh.
In 2000, the UK government received a windfall of around £23 billion from its auction of third generation (3G) mobile phone licences. This astronomical sum wasn't the result of corporate bidders "losing their heads", but a careful strategy designed to maximise proceeds for the Treasury.https://huffduffer.com/adactio/6639
https://huffduffer.com/adactio/6639
Thu, 23 Jul 2009 13:40:56 GMTmathematicsfive numbersbook:author=simon singhbbcgame theoryKepler's ConjectureEpisode four of Another Five Numbers, the BBC radio series presented by Simon Singh.
Johannes Kepler experimented with different ways of stacking spheres. He concluded that the "face-centred cubic lattice" was best. Using this method, Kepler calculated that the packing efficiency rose to 74%, constituting the highest efficiency you could ever get. But, how to prove it?https://huffduffer.com/adactio/6613
https://huffduffer.com/adactio/6613
Wed, 22 Jul 2009 08:50:57 GMTmathematicsfive numbersbook:author=simon singhbbckepler's conjectureThe Largest Prime NumberEpisode three of Another Five Numbers, the BBC radio series presented by Simon Singh.
Think of a number. Any number. Chances are you haven't plumped for 2 to the power of 13,466,917 -1. To get this, you would need to keep multiplying 2 by itself 13,466,917 times, and then subtract 1 from the result. When written down it's 4,053,900 digits long and fills 2 telephone directories. So, as you can imagine, it's not the kind of number you're likely to stumble over often. Unless you're Bill Gates checking your bank statement at the end of the month. https://huffduffer.com/adactio/6588
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Tue, 21 Jul 2009 08:36:37 GMTmathematicsfive numbersbook:author=simon singhbbcprimesThe Number SevenEpisode two of Another Five Numbers, the BBC radio series presented by Simon Singh.
Picture a gambler. Is it George Clooney, tuxedo ruffled after an all-nighter at a Vegas Black Jack table, or your old Aunt Doris putting down her yearly quid-on-the-nose for the Grand National? Recent research would suggest that it's neither. Your inveterate gambler is far more likely to be sporting leather patches at their elbows, an unhealthy appetite for corduroy, and a penchant for M-Series rather than Martinis, shaken or stirred. Some mathematicians are putting their mathematical theory where their mouth is and are betting the shirts, stuffed or otherwise, off their backs.https://huffduffer.com/adactio/6549
https://huffduffer.com/adactio/6549
Sun, 19 Jul 2009 13:54:17 GMTmathematicsfive numbersbook:author=simon singhbbcsevenThe Number FourEpisode one of Another Five Numbers, the BBC radio series presented by Simon Singh.
Simon Singh's journey begins with the number 4, which for over a century has fuelled one of the most elusive problems in mathematics: is it true that any map can be coloured with just 4 colours so that no two neighbouring countries have the same colour? This question has tested some of the most imaginative minds — including Lewis Carroll's — and the eventual solution has aided the design of some of the world's most complex air and road networks.https://huffduffer.com/adactio/6495
https://huffduffer.com/adactio/6495
Wed, 15 Jul 2009 23:39:37 GMTmathematicsfive numbersbook:author=simon singhbbcfourInfinityEpisode five of Five Numbers, the BBC radio series presented by Simon Singh.
Given the old maxim about an infinite number of monkeys and typewriters, one can assume that said simian digits will type up the following line from Hamlet an infinite number of times.https://huffduffer.com/adactio/6452
https://huffduffer.com/adactio/6452
Tue, 14 Jul 2009 12:21:49 GMTmathematicsfive numbersbook:author=simon singhbbcinfinityThe Imaginary NumberEpisode four of Five Numbers, the BBC radio series presented by Simon Singh.
The imaginary number takes mathematics to another dimension. It was discovered in sixteenth century Italy at a time when being a mathematician was akin to being a modern day rock star, when there was 'nuff respect' to be had from solving a particularly 'wicked' equation. And the wicked equation of the day went like this: "If the square root of +1 is both +1 and -1, then what is the square root of -1?"https://huffduffer.com/adactio/6445
https://huffduffer.com/adactio/6445
Tue, 14 Jul 2009 08:02:21 GMTmathematicsfive numbersbook:author=simon singhbbcimaginary numberThe Golden RatioEpisode three of Five Numbers, the BBC radio series presented by Simon Singh.
Divide any number in the Fibonacci sequence by the one before it, for example 55/34, or 21/13, and the answer is always close to 1.61803. This is known as the Golden Ratio, and hence Fibonacci's Sequence is also called the Golden Sequence. Unlikely though it might seem, this series of numbers is the common factor linking rabbits, cauliflowers and snails.https://huffduffer.com/adactio/6411
https://huffduffer.com/adactio/6411
Sun, 12 Jul 2009 18:08:23 GMTmathematicsfive numbersbook:author=simon singhbbcgolden ratiofibonacciSimple as PiEpisode two of Five Numbers, the BBC radio series presented by Simon Singh.
Most people's first slice of Pi is at school where it is generally made palatable as either 3.14 or the fraction 3 1/7. The memory of this number may be fuzzy for those propelled through their Maths GCSE by the power of Casio (where Pi was reduced to a button on the bottom row of the calculator), but the likelihood is they still recall that romanticised notion of a number whose decimal places randomly go on forever. At its simplest, Pi is the ratio of the circumference of a circle to its diameter. At its most complex, it is an irrational number that cannot be expressed as the ratio of two whole numbers and has an apparently random decimal string of infinite length.https://huffduffer.com/adactio/6408
https://huffduffer.com/adactio/6408
Sat, 11 Jul 2009 18:21:57 GMTmathematicsfive numbersbook:author=simon singhbbcpiA Countdown to ZeroEpisode one of Five Numbers, the BBC radio series presented by Simon Singh.
What's 2 minus 2? The answer is obvious, right? But not if you wore a tunic, no socks and lived in Ancient Greece. For strange as it sounds, 'nothing' had to be invented, and then it took thousands of years to catch on.https://huffduffer.com/adactio/6384
https://huffduffer.com/adactio/6384
Thu, 9 Jul 2009 21:50:53 GMTmathematicsfive numbersbook:author=simon singhbbczero