Mathematics at top speed
QUESTION In the recent film Gifted, one of the characters uses the Trachtenberg system of calculating maths problems. Is this a real system? How does it work and who developed it? THE Trachtenberg system was a method of speed mental arithmetic developed by the Russian mathematician Jakow Trachtenberg while he was in a Nazi concentration camp.
He was born in Odessa – then part of the Russian Empire, now in Ukraine – on June 17, 1888. Graduating from the prestigious Berginstitut of St Petersburg, he rose to become chief engineer at the Obuschoff shipyards.
A critic of the Russian revolution, he fled to Germany disguised as a peasant in 1919 and married an aristocrat.
With the emergence of fascism, Trachtenberg spoke out against Hitler and, in 1934, accompanied by his wife, he escaped to Vienna. He was taken prisoner when the Germans annexed Austria, but managed to escape briefly to Yugoslavia. Caught again, he spent the war in various concentration camps.
To escape the misery surrounding him, he took refuge in his mind and developed his system of mental arithmetic.
In 1945, Trachtenberg and his wife escaped into Switzerland, where he perfected his system and dedicated the rest of his life to teaching it to disadvantaged children. Andrew Vernon, Norwich. JAKOW TRACHTENBERG’S mathematical system was published in English in 1960. The Trachtenberg Speed System of Basic Mathematics is a way of performing high-speed multiplication, division, addition, subtraction and square root, all in your head.
Here is one example of his method, showing how to mentally calculating multiples of 11. Take 1,342 x 11: You can get the answer using these rules:
1. The last number of the multiplicand – a number that is to be multiplied by another (the multiplier) – 1,342 is 2 and this will be the right hand figure of the answer: 2.
2. Each successive number of the multiplicand is added to its neighbour to the right. So for 1,342, we start by adding 4 to 2 and we calculate the second figure of the answer: 62. We can then add 3 to 4 to give the third: 762. And again we can add 1 to 3 to give the fourth: 4,762.
3. The first number of the multiplicand becomes the left-hand number of the answer: 1. So the answer is 14,762. Keith Perry, Nottingham. QUESTION Where was the world’s first working nuclear power station? THE Idaho National Laboratory made history on December 20, 1951, when a row of four 200-watt light bulbs lit up in a nondescript brick building. The electricity to power them came from a generator connected to Experimental Breeder Reactor I. This was the first time a usable amount of electrical power had been generated from nuclear fission.
The first commercial nuclear power plant was Calder Hall in Sellafield, Cumbria, north-west England, and was developed due to the British military need for plutonium. Having decided in 1947 to build atomic weapons, Britain opted for a version of the plutonium-based bomb dropped on Nagasaki.
Winston Churchill was prime minister in 1953 and had failed to obtain a supply of bombs from US president Dwight D Eisenhower. He sanctioned the construction of the first Pressurised Pile Producing Power and Plutonium at Calder Hall. The name reflected its dual role to produce weaponsgrade plutonium and commercial nuclear energy. It began generating electricity on August 27, 1956.
Each of the first two Magnox reactors could produce 65MW of electrical energy, and two more were added later. Magnox fuel is so-called because of its magnesium alloy cladding – the chemical reactivity of this means the fuel can’t be stored indefinitely.
Though Magnox reactors were initially dual purpose, from 1964 plutonium production was confined to another facility at Windscale. When Calder Hall closed on March 31, 2003, the first reactor had been in use for nearly 47 years. Derek Purnell, Cumbria. QUESTION What was the last letter added to the alphabet? THE letter ‘J’, adopted in the 16th century, was the last letter added to the alphabet.
Classical Latin did not have a ‘J’ sound; it used ‘I’ to represent a vowel sound (as in machine) and a consonant (as in yellow).
In the Roman/Latin alphabet, the English alphabet’s predecessor, ‘j’ wasn’t a letter, but a swash, a typographical flourish added to the letter ‘I’.
By the 1500s, speakers of the languages such as Italian noted the confusion that resulted from this.
In 1524, Gian Giorgio Trissino, an Italian Renaissance grammarian, recommended the Roman swash ‘j’ be used as a consonant in its own right. His innovation was quickly adopted. Edward Woodridge, Oxford.
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