Incredible Formula - Numberphile

Dr James Grime discusses a couple of clever formulas which are pandigital - using all the numbers from 1-9.
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NUMBERPHILE

Videos by Brady Haran

[nichrun]

Numberphile. The only channel where a formula is described as "cute". So adorable.

[wilkatis]

How to remember e to more decimal places than you'll ever need?
It's 2 point 7 followed by birth year of Lev Tolstoj (1828) followed by birth year of Jules Verne (1828) followed by angles of isosceles right triangle (45 90 45)
e = 2.7 1828 1828 45 90 45 ...
Now you can't say I didn't learn anything at mathematics class

[rajajinnah]

0:14
So 'Zero' is basically me during my friends' road trips 😂

[itsnotcharan]

To blow your mind:

81= 9^2= 3^4=70+6+5

[Anamnesia]

4:15 "I Love e SO much..."
Me too, but I don't go around telling everyone about it!

[steliostoulis]

love Dr Grime. ...his enthusiasm is so relatable

[GtaRockt]

2 Dr. Grime videos in a row? It's almost like it's Christmas!

[ImaginaryHuman]

For those asking for full steps:

3^(2^85) = 3^[2*(2^84)] = (3^2)^(2^84) = 9^(2^84) = 9^[2^(2*42)] = 9^[(2^2)^42] = 9^(4^42) = 9^[4^(6*7)]

[codediporpal]

1:20 I case you were wondering, Dr. James Grime was actually calculating that number on the fly, from the equation, while talking to you.

[ganaraminukshuk]

Can we call approximations of e E-proximations?

[andrewkovnat]

I wonder what that paper feels like...
That is life's biggest question.

[david-ytoo]

I smiled when he mentioned how accurate it was

[MrCyanGaming]

If you're reading this, have an amazing Christmas! 🎄🎄🎄

[EclecticSceptic]

Wow that's an amazing formula. The precision is remarkable.

[AlexRomanov]

he gets so happy about numbers, its adorable. lol

[filipsperl]

I don't see why everyone has a problem with the 6*7 not just being 42. First, the mathematical curiosity explored in this video is not a formula, but a number. The whole thing can be expresed as one number, which is very close to e. Every part of the number can be expressed differently and it doesn't matter what signs, brackets or symbols are between them. If 4^2 were to show up in these type of expressions, of course you can write it just as 16, but you need the digits 4 and 2, just as you need 6 and 7 in this case. Why would that be considered cheating?

[Philgob]

Amazing! So simple yet it's very impressive that he was able to do this.

[astropgn]

If you put e / ((1+9^(-4^(6*7)))^3^2^85) on wolfram alpha, the result is "e"... weird

[LVo]

That last formula was such a parker square...

[camilohiche]

Those pandigital formulas are kinda parker squared though tbh...