One Factorial!
For you that don't know the mathematical function, factorial (! as a symbol), is essentially multiplying a number by all of the figures lower than it. I myself, do not know why this is useful but it is. Now, you would think that zero factorial is zero (as 0 x -1, -2, ... = 0), but it is not!
The reason behind this is that it completes a pattern! I cant explain it myself but see this video to see the full explanation.
This article was written by Liam Scaife.
The reason behind this is that it completes a pattern! I cant explain it myself but see this video to see the full explanation.
This article was written by Liam Scaife.
How to add up a lot of sequential numbers
In case you do not know what sequential numbers are, they are something like 1, 2, 3, 4, 5, 6, 7, 8, 9... and so on.
So how to add up the numbers?
Well say you wanted to add up the numbers on a dice (1+2+3+4+5+6) so you say that n = 6, so the formula for this is n x (n+1) over two, so you go 6 x 7 = 42 divided by 2 is 21 and that is your answer, so simple!
This article was written by Nicholas Cranefield.
So how to add up the numbers?
Well say you wanted to add up the numbers on a dice (1+2+3+4+5+6) so you say that n = 6, so the formula for this is n x (n+1) over two, so you go 6 x 7 = 42 divided by 2 is 21 and that is your answer, so simple!
This article was written by Nicholas Cranefield.
Infinite Primes
Prime numbers are amazing, I love them. There beautifully complex, and have so many sub-topics! Primes are essentially, any integer that can only be divided by one and itself (I have a comprehensive list and explanation over on the prime number page).
Lets assume that there where finite primes, that meaning we could list all of them. We have a new list, p1, p2, p3, p4..., pn. Now we define a new number (Q), that is all the primes multiplied together plus one. If this new number is a prime, we have a problem (as this would be a new prime that is not on our list). If it is not, then all the primes should be able to evenly divide Q. But due to the nature of primes, none of the primes divide Q evenly, so this means that the list is not complete.
If there where finite primes, then you be able to have a complete list. And this is the proof that there are infinite primes.
This article was inspired by Dr. J Grime over on Numberphile.
This article was written by Liam Scaife.
Lets assume that there where finite primes, that meaning we could list all of them. We have a new list, p1, p2, p3, p4..., pn. Now we define a new number (Q), that is all the primes multiplied together plus one. If this new number is a prime, we have a problem (as this would be a new prime that is not on our list). If it is not, then all the primes should be able to evenly divide Q. But due to the nature of primes, none of the primes divide Q evenly, so this means that the list is not complete.
If there where finite primes, then you be able to have a complete list. And this is the proof that there are infinite primes.
This article was inspired by Dr. J Grime over on Numberphile.
This article was written by Liam Scaife.
Pi
Many of you will know of Pi as simple 3.14, but there is more!
Pi is an irrational number, meaning that it is infinite. Mathematicians have calculated about ten trillion decimal places of Pi (with computers of course). Some people (like myself) have found it great fun to memorize as much as we can, i can only resit about sixty three decimal places. Some people have pushed there minds to the limits with up to four thousand decimal places!
Pi is used to calculate the areas, diameters and circumferences of circles and spheres. Surprisingly it only takes thirty nine places to calculate the area of the observable universe (down to the size of one hydrogen atom)!
Pi continues to be an everyday part of our lives, just imagine how many circles are around you all the time!
This article was written by Liam Scaife.
Pi is an irrational number, meaning that it is infinite. Mathematicians have calculated about ten trillion decimal places of Pi (with computers of course). Some people (like myself) have found it great fun to memorize as much as we can, i can only resit about sixty three decimal places. Some people have pushed there minds to the limits with up to four thousand decimal places!
Pi is used to calculate the areas, diameters and circumferences of circles and spheres. Surprisingly it only takes thirty nine places to calculate the area of the observable universe (down to the size of one hydrogen atom)!
Pi continues to be an everyday part of our lives, just imagine how many circles are around you all the time!
This article was written by Liam Scaife.