What's special about 288? - Numberphile

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NUMBERPHILE

Video by Brady Haran and James Hennessy

[ceegers]

For the notation, we could go in a spanish direction and do ¡4! for superfactorial of 4.

[yoru]

It's even cooler when you realise sf(4) can be written as 4^1 x 3^2 x 2^3 x 1^4.
So sf(4) = 4^1 x 3^2 x 2^3 x 1^4 = 288 = 4^4 + 3^3 + 2^2 + 1^1

[fechtbrandon]

Notation suggestion: Using an exclamation point after but instead as a superscript. This makes sense (to me, at least) since superfactorials are repeated factorialization in a similar way that exponentiation is repeated multiplication. And "superscript" uses the word super! e.g. 4^! = 288

[methethpropbut]

As a long-time viewer of Numberphile (about 8 years and counting!) it's quite surreal seeing someone I used to see in uni lectures make it famous on here. Thank you for continuing to spread the love of mathematics to a new generation.

[xcheese]

You're doing a Numberphile video about 288? I think it's two gross.

[Luperbillion]

I feel like the favorite number videos is closest to the spirit of Numberphile. You get some much passion from their explanation

[tttITA]

Mix the dollar sign with an exclamation point! So it has an "s" for "super" and a "!" for factorials.

[veqv]

Calling it now. This woman is the next Hannah Fry. Wonderful exposition - anticipates the reader, has fun quips and keeps folks engaged.

[Verlisify]

Does a mathematician ever hear a new number fact and not make it their new favorite number

[gabor]

Thank you, very cool! Fun fact: 288 is twice 144 which is 12 squared and is the 12th Fibonacci number.

[Matthew-bufg]

If maths doesn't work out for Sophie then there's always scriptwriting - there were so many twists in this video before the crescendo! 😆in all seriousness, I loved the enthusiasm!

Also love that we've got what I like to think as a "classic numberphile" video. A fairly run of the mill, bog standard base ten number that we never think about but - when unpicked - turns into something beautiful!

[OrangeC]

This Numberphile video in particular has a playfulness to it that I think is absolutely awesome, one of my favourites already!

[goodboi]

Is it not confusing to use n!! notation as given in the video as opposed to taking a factorial twice (as in, factorial of n!)? The second one seems like a more obvious way to interpret the double exclamation.

[Wolforce]

Suggestion for notation. Since it's supposed to be super, it should be a buffed up exclamation mark. That could be a triangle (inverted delta) with a bold dot at the bottom. Like a comics BAM exclamation mark

[SRangerMtl]

My favorite mathematician changes a lot, but for now it is Sophie Maclean.

[Oler-yxxj]

If we have run out of Latin and Greek alphabets, we can use something like 超 for superfactorial

[johnchessant]

That's pretty cool! And I think the sf notation is perfectly fine, since in music sf means "sforzando", which tells you to play a note with a sudden emphasis!

[joshuazelinsky]

288 has some other nice properties also. It is a refactorable number, which is a number whose total number of positive divisors is itself a divisor of the number. (A smaller example is 12 which has 6 divisors one of which is 6).

288 also is one of the rare numbers which are both twice perfect square and one less than a perfect square. There are infinitely many of these and they connect to what is known as Pell's Equation.

[michaels]

6:20 It's square because it's an even power, not because it's a power of two.

[jasonremy]

It's been a while since we've had an OG Numberphile video about an actual number! Love it!