## Illustrated Math Function

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Bloopy
Posts: 217
Joined: Wed May 04, 2011 9:16 am UTC
Location: New Zealand

### Illustrated Math Function

I take a mathematical function and run it on each number from a set of four consecutive integers. Unfortunately the universe is being particularly hostile today, and returns the output as four images that crudely represent each of the four answers.

If you think you know the function I used, describe or suggest images that could fit immediately before and after the four I have. thefargo
Posts: 36
Joined: Mon Jan 20, 2014 3:45 pm UTC

### Re: Illustrated Math Function

My thoughts:
Spoiler:
The first image is 0
The second image somehow involves x? Though I guess its supposed to be a number. I'm pretty sure this is an x-ray of a large truck. Maybe 18 (for 18 wheeler)?
The third images is either pi^2 or pi/6

Just getting the juices flowing

Pelli
Posts: 22
Joined: Fri Jun 26, 2009 6:02 am UTC

### Re: Illustrated Math Function

thefargo wrote:My thoughts:
Spoiler:
The first image is 0
The second image somehow involves x? Though I guess its supposed to be a number. I'm pretty sure this is an x-ray of a large truck. Maybe 18 (for 18 wheeler)?
The third images is either pi^2 or pi/6

Just getting the juices flowing

Interesting observation on the third image. I would guess it's
Spoiler:
pi^2/6 = 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = zeta(2)
just because that's a famous number.
( http://en.wikipedia.org/wiki/Particular ... a_function )

EDIT: Expanding on this...
Spoiler:
zeta(0) = -1/2
zeta(1) = gamma (Euler-Mascheroni constant)
zeta(2) = pi^2/6
zeta(3) = Apéry's constant

As for the links with the pictures:
zeta(0): ???
zeta(1): A Google image search of "gamma ray imaging" yields the picture as the first result.
zeta(2): It's a sixth of a square pie.
zeta(3): The picture depicts apery of an ape?

To extend the sequence:
zeta(-1) = -1/12 [???]
zeta(4) = pi^4/90 [a hypercube pie cut into 90 pieces?]

thefargo
Posts: 36
Joined: Mon Jan 20, 2014 3:45 pm UTC

### Re: Illustrated Math Function

Bravo! Certainly you've hit on the correct answer. As for the images,

Spoiler:
Note that pi^4/90 is equal to the sum from n = 1 to infinity of 1/n^4. Perhaps this would be easier to express as an image?
and -1/12 is the Ramanujan Sum of the natural numbers (1+2+3+...)

edit:
http://www.archimedes-lab.org/images8/N ... arabic.gif

Bloopy
Posts: 217
Joined: Wed May 04, 2011 9:16 am UTC
Location: New Zealand

### Re: Illustrated Math Function

In case you want a little push in the right direction, these are correct:

Spoiler:
thefargo wrote:The first image is 0

Pelli wrote:pi^2/6

These need a bit of manipulation:

Spoiler:
Pelli wrote:gamma (Euler-Mascheroni constant)
Apéry's constant

Pelli
Posts: 22
Joined: Fri Jun 26, 2009 6:02 am UTC

### Re: Illustrated Math Function

An obvious guess for a bit of manipulation of the second image is
Spoiler:
It's the negative (and possibly half?) of the original, so -gamma or -gamma/2.

thefargo
Posts: 36
Joined: Mon Jan 20, 2014 3:45 pm UTC

### Re: Illustrated Math Function

Another interpretation is:

Spoiler:
the colors are inverted, so its gamma inverted, which is 1/gamma

Bloopy
Posts: 217
Joined: Wed May 04, 2011 9:16 am UTC
Location: New Zealand

### Re: Illustrated Math Function

Since it's quietened down, I'll point out that this number is correct too:

Spoiler:
Pelli wrote:-gamma

Bloopy
Posts: 217
Joined: Wed May 04, 2011 9:16 am UTC
Location: New Zealand

### Re: Illustrated Math Function

Answer enclosed here for the record:
Spoiler:
The images were obtained using the polygamma function: y = ψ(x)(1), for x = -1 to 2.

The two primates are frowning (negative), giving -2*Apéry's constant.

The first missing image could be quite gross considering a log of the number 2 is involved. The last could be a 1/15th slice from mom's old-fashioned pecan tesseract, similar to what Pelli suggested.