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#1 Re: Euler Avenue » Anyone know of a function like this? » 2013-05-02 01:34:21

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

#2 Re: Euler Avenue » Anyone know of a function like this? » 2013-05-01 05:07:28

It appreciates being addressed by unsaid name.

#4 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-30 00:12:12

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?

#5 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-29 07:21:05

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.

#6 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-29 07:02:44

What type(s) of function(s) would it be? I assume it is a power function and an exponential function.

#8 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-25 23:59:58

Very true. I guess if I represent it as

y = |x|^[1-|x|]  from x=-5 to 0

It looks more simple and orderly

#9 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-25 23:03:09

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

#10 Re: Euler Avenue » Was mathematics invented or discovered? » 2013-04-25 22:21:24

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?

#11 Re: Euler Avenue » Anyone know of a function like this? » 2013-04-25 21:57:03

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).

#12 Euler Avenue » Anyone know of a function like this? » 2013-04-25 03:49:24

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

#14 Re: Euler Avenue » Ramanujan's pi approximation equation » 2013-01-04 02:07:08

Here's one that increases it another ten-fold... 131^[5131/21852] ≈ 3.141592653555866563449102187233485139443062510610029...

#15 Re: Euler Avenue » Ramanujan's pi approximation equation » 2013-01-04 01:51:15

Accuracy doesn't increase ten-fold again until 41^[5429/17612]≈3.1415926536893...

#16 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-04 00:36:10

Sorry about that. Each triple (2013 to 2015, 1885 to 1887 and 2665 to 2667) has numbers with exactly three distinct prime factors each.

#17 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-03 07:07:41

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.

#18 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-03 06:18:26

Interesting that 2013 is composed of four sequential digits: 0, 1, 2 and 3. That hasn't happened since 1432... 581 years ago!

#19 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-03 05:41:54

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. smile

#20 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-03 01:15:39

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

#21 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-02 11:24:37

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!

#22 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-02 06:27:54

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 smile

#23 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-02 04:06:18

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

#24 Re: Dark Discussions at Cafe Infinity » Happy 2013 » 2013-01-02 03:27:58

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"?

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