Mental ‘Abacus’ Calculation Technique

Amazing calculation technique of Indian kids:

It is the advanced level of abacus calculation, whereby the physical abacus is replaced by a virtual abacus in the mind — see the kids need to move their fingers in the air, as if they touch a real abacus. The display of the workings (moving up and down of the abacus beans) in the mind is like seeing the abacus image from a computer screen. It means also the kids are still not mentally calculating per se, they just continue to calculate on the ‘virtual’ abacus.

This is different from a real mental calculation sans a physical electronic calculator, in which case no fingers playing the pressing buttons of an electronic calculator. The brain is the real calculator, with some helps of math tricks and shortcuts.

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Open Cubic Root

Mental Trick

It was discovered by the Martial Art writer Liang Yusheng 武侠小说家 梁羽生 (《白发魔女传》作者), who met Hua Luogeng (华罗庚) @1979 in England:
2³= [8]
8³= 51[2]
3³= 2[7]
7³= 34[3]

The last digit pairs :
[2 <->8] , [3 <-> 7]
Others unchanged.

Example:

\sqrt[3]{658503} = N
Last three digits 503 <-> …[7]
First three digits 658:
 (8³ =512)< 658 < (729 = 9³)
=>  8
Answer : \sqrt[3]{658503} = N= 87
Note: Similar trick for opening \sqrt[23] {200 digits} by an indian lady Ms Shakuntala (83) dubbed “Human computer”.

Indian Lady Shakuntala

Human computer