Every integer >5 can be expressed as the sum of 3 primes
Because I find that really beautiful, but then I realised that this was still just a conjecture.
Whoops!
]]>Βεν Γ. Κυθισ wrote:Do you mean rather than ?it should be (a^m)n^a.
DANG IT! I forgot to move the variables around! And I forgot to confirm it with a calculator or my miiiiind.
]]>Do you mean rather than ?]]>it should be (a^m)n^a.
Hi Βεν,
Welcome to the forum! Thanks for your contribution. That looks like a nice list. Some comments:
I know what you mean, but this can be misleading: is multiplied by itself times. For example, , where gets multiplied by itself one time.a^n=a multiplied by itself n times
The brackets should go around the here, i.e. for even .If n is even then (-a^n)=a^n
On one side of the equation, the and are the wrong way round. It should read:a^n÷a^m=a^(m-n) (Makes sense right?)
If n>0 then (a^m)na=a^(m+n)
What did you mean here?
I fixed my errors and typos. My answer to
What did you mean here?
is that I messed up; it shouldn't be (a^m)na, it should be (a^m)n^a. I feel so stupid for not checking with a calculator.
]]>Welcome to the forum! Thanks for your contribution. That looks like a nice list. Some comments:
a^n=a multiplied by itself n times
If n is even then (-a^n)=a^n
a^n÷a^m=a^(m-n) (Makes sense right?)
If n>0 then (a^m)na=a^(m+n)
What did you mean here?
]]>But mathamaticans have calculated that if you have some 200 000 -dimensional shape (just a big number idk), it doesen't follow the regular symmetry logic so far. It form's its own group of symmetry, sometimes referred as monster group, and is not the only instance when it happens.
It is really hard to think what is really going on there, but John Convay himself thinks (somewhere in lines of) these obejcts like a christmas tree decorations; like this some regular shape, with some faces some going that way, some horizontally, some verticlaly, some in high-dimensional directions, but also unexpectelly in THIS direction.
]]>The set contains all complex numbers, which if infinitely raised to power of 2 and added the initial value to, don't blow up to infinity but converge to a value.
You can also create another fractal, or halo, around the set if you plot the last breakpoint value.
If you think that every function transforms 2D plane's every point, the act of complex exponentation will bend the straight lines invards infinitely. With negative values the numbers close to zero explode close to infinity and wise versa.
You can also create other fantastic fractals with similar equations, namely, {iterated = iterated ^ start + start}, {iterated = start ^ initerated}, {iterated = -iterated ^ iterated}, {iterated = sqrt(iterated)+initial}
just to name a few. With some of these the halos are more incredible than the actual set.
1. A number of the nth row and nth position getting found out by Combiantion.
2.Existence of Fibonacci Sequence as bob showed above.
3.Shading Odd nos. in a Pascal's Triangle gives Sierpenski triangle series.
4.HCF of any row of a prime no. excluding 1 is that prime no. itself.
5.If you draw a hockey stick starting from an extreme end (that is a 1)and make a Hockey Stick,with only 1 number in the "J", the sum of all nos. in the stick = to the no. in the "J" of the hockey.
6.Adding nos. of the nth row give value as (2^n)
7.The nos. of the 2nd diagonal are the counting nos., the nos. in the 3rd diagonal are triangular nos., in the fourth are tetrahedral nos. and so on
8.The nos. of the nth row are the digits of 11^n.(From 11^5, it begans to overlap itself)
9.The pascal's triangle is symmetrical
10.Existence of catalan nos.
11.Pick any number inside Pascal’s triangle and look at the six numbers around it (that form alternating petals in the flowers drawn above). If you multiply the numbers in every second petal, you’ll end up with the same answer no matter which of the petals you start from.
12.Pick any counting number from along the first diagonal and square it. Then look at its two neighbours that lie deeper inside the triangle – they’ll always add up to that very same square number.
13.If you add up every single number in the first n rows, you’ll get the nth Mersenne number.
]]>Yeah I know it.
This is one of the 7 things of the pascals triangle which i find very interesting.
What are the other 6?
]]>325 is the smallest number to be the sum of two squares in 3 different ways:
and .425 also has a similarly property :
]]>This is one of the 7 things of the pascals triangle which i find very interesting.
]]>