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Just playing on a variation of this unsaid function...

y = |x^x|

Isn't it neat that the local minima of the doman -5<=x<=5 is e^[-1/e] at x = 1/e?

Here's a link to the calculation:

http://www.wolframalpha.com/share/clip?f=d41d8cd98f00b204e9800998ecf8427evkrcm4invi

It appreciates being addressed by unsaid name.

Thanks!

bobbym wrote:

Hi;

You mean this expression?

You mean is it a function? Or would you like to approximate that with a something else?

Yup, I mean, is it a function or what kind of function is it?

Would it be a power function because it is y = | x ^...|

...likewise, would it be an exponential function because it has a variable in the exponent? Just curious.

Whoa! That is good, bobbym. Thank you!

Very true. I guess if I represent it as

y = |x|^[1-|x|] from x=-5 to 0

It looks more simple and orderly

That's true... do you have an equation in mind?

n872yt3r wrote:

I think it was invented, because numbers don't exist. They are a placeholder we use for a certain amount. They're not exactly one thing, if they were, shape-shifting could exist, because numbers would be everywhere. They're sort of a principle.

The idea of a placeholder makes sense.

Objects counted any other way would still be just as numerical. The numerical quality itself perhaps comes with objects being physical. There might be 1 x 10^80 atoms in the physical universe ... it's an intrinsic quality/principle of the universe, we might say?

**pellerinb**- Replies: 25

Hi all,

I have this function's shape in mind...

plot y = |(x-5)|^[1-|(x-5)|] from x=0 to 5

Anyone seen this kind of curve before in a similar (i.e. simpler) function? I really had to "mess around" to make it lol!

math is fun! :-D

7907 - 6907

**3.1415926535**55866563449102187233485139443062510610029...

Accuracy doesn't increase ten-fold again until 41^[5429/17612]≈**3.141592653**6893...

The article's comments also have

41^2 + 19^2 - 5^2 - 2^2

43^2 + 17^2 - 11^2 - 2^2

curious if I can pull it off with just three.

True, it might be erroneous but it's worth claiming just for the inspiration!

Found it! Seems like 2013 = 47^2-19^2+13^2-2^2

So it can be made up by only 4 prime squares! Cool!

Yes, and I just got a message from one of the authors on the explanation:

"2013 is the smallest number that needs at least six squares to make."

That means that 2013 is the smallest number that *requires* at least six squares to produce. Yes, there are smaller numbers that can be made with six squares. But all of those numbers can also be made with five or fewer squares

Anyone know how John Chew came up with this statement:

"2013 is the smallest number that is at least six added or subtracted squares of prime numbers."

in his webpage article, "How is 2013 interesting? Let us count the ways"?

Hehe. Exactly.