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.

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.


\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