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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!
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.
What type(s) of function(s) would it be? I assume it is a power function and an exponential function.
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?
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?
Yes... so... I'm just wondering if you have seen this shape elsewhere in a simpler function (I'm not considering the rest, just this part of the plot as you got).
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
Here's one that increases it another ten-fold... 131^[5131/21852] ≈ 3.141592653555866563449102187233485139443062510610029...
Accuracy doesn't increase ten-fold again until 41^[5429/17612]≈3.1415926536893...
Sorry about that. Each triple (2013 to 2015, 1885 to 1887 and 2665 to 2667) has numbers with exactly three distinct prime factors each.
Also interesting is that 2013 to 2015 are consecutive numbers each with unique factors. That happened last in 1885-1887 and happens again in 2665-2667.
Interesting that 2013 is composed of four sequential digits: 0, 1, 2 and 3. That hasn't happened since 1432... 581 years ago!
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!
I believe so. Otherwise, I suppose there's a way to stuff in a bunch of small 2^2's and 3^2's to fill in the gaps... Can't use any 2^1's though... I believe that's cheat'n
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.