As a first post, my role is to be meaningless and unoriginal.
Seriously though, if you're interested in maths, you should have some fun following this thing. At this stage everything will be in layman's terms, with minimal mathematical jargon, so that people who aren't immersed in maths can still enjoy it. It won't be fully active until mid to late November, as until then I have exams to contend with, but once that's done, this will hopefully be an active blog.
Until then, I'll post something cool that my maths lecturer showed me.
What's the sum of all of the natural (read whole numbers greater than 0) from 1 to n? Up to, say, 10, we can do without too much effort but when adding to 256 (my favourite number) or 2034986 this becomes more difficult.
We were asked to find the sum of the numbers from 1 to 100. I paired numbers that added to give 100, and it's not too hard to see that there are 49 of these (1 and 99, 2 and 98... all the way to 49 and 51). 49*100 is 4900. Then you add the 50 and the 100 that you've skipped out on and voila, 5050 is spat out. This took me around 20 seconds, but Gauss managed this in similar time when he was 6. This is supposed to be something like what he did.
Lets say we want to add the numbers from 1 to 4. The answer is obviously 10. Let's stack them in a triangle.
A good estimation for the number of dots is the area of the triangle made by them. This has base length 4 and height 4. Using the formula A=1/2*base*height, we find that the estimated area is 8. It's close, but it's not quite right. Here's the cool part. What happens if you put another one of these triangles on top of the first one?
Seriously though, if you're interested in maths, you should have some fun following this thing. At this stage everything will be in layman's terms, with minimal mathematical jargon, so that people who aren't immersed in maths can still enjoy it. It won't be fully active until mid to late November, as until then I have exams to contend with, but once that's done, this will hopefully be an active blog.
Until then, I'll post something cool that my maths lecturer showed me.
What's the sum of all of the natural (read whole numbers greater than 0) from 1 to n? Up to, say, 10, we can do without too much effort but when adding to 256 (my favourite number) or 2034986 this becomes more difficult.
We were asked to find the sum of the numbers from 1 to 100. I paired numbers that added to give 100, and it's not too hard to see that there are 49 of these (1 and 99, 2 and 98... all the way to 49 and 51). 49*100 is 4900. Then you add the 50 and the 100 that you've skipped out on and voila, 5050 is spat out. This took me around 20 seconds, but Gauss managed this in similar time when he was 6. This is supposed to be something like what he did.
Lets say we want to add the numbers from 1 to 4. The answer is obviously 10. Let's stack them in a triangle.
A good estimation for the number of dots is the area of the triangle made by them. This has base length 4 and height 4. Using the formula A=1/2*base*height, we find that the estimated area is 8. It's close, but it's not quite right. Here's the cool part. What happens if you put another one of these triangles on top of the first one?
Turns out what you get is a rectangle of area 5*4=20. Remember that we want to find the area of half the rectangle, which is of course 20/2=10.This can, of course, be generalised into something easy to use. Turns out that, if you let n=the highest number you add to, if you add up all the numbers from 1 to n, you can calculate this using the formula below.
Sum of all numbers from 1 to n =
Using this formula, we can fund out the sum of all the numbers up to 256.256*257/2=32896
Well, that's the first of many I expect. There will probably be a few on infinite series to come, since we spent the last little while doing that at uni. Until then, salut :)
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