And ooh I meant to comment on this. There are soo many cool patterns in Pascal's Triangle! And using the Golden Ratio is ahhh so many cool things in each of these alone!!
You really need to make a math blog as well
Yes, both of these are extremely exciting!!
If anything, I would love to add to a wiki if you ever happen to make anything a wiki!
That sounds like an amazing idea, so I'll change it right now! This is exciting
Actually, I'll create a post down here as well so we can work on some of the posts
The Golden ratio blog post:
- The Golden Ratio is equal to
(1 + √5)/2 : 1, which is approximately
1.618... : 1. The number is also known as phi Φ, a letter of the Greek alphabet (like how pi π is also a letter of the Greek alphabet, and phi rhymes with pi).
(it's a matter of opinion), but shapes using the Golden Ratio for measurements are thought to be aesthetically pleasing, hence the name. e.g. a rectangle with its side lengths in the Golden Ratio, with the longer side 1.618 in comparison to the shorter side is known as a golden rectangle.
If you take any two consequential Fibonacci numbers and divide the smaller one into the larger one, as the Fibonacci numbers grow larger, it will get closer and closer to the golden ratio!
if you add 1 to phi you get its square, and if you subtract 1 from phi you get its reciprocal (recipocral is when you divide 1 by a number)
Please excuse my handwriting for Φ
[insert maths pages]
Golden Ratio in graphics design (but it does mention the basics and reminded me of how the Golden Ratio appears in nature!)
Yaay!!!! I remember when I first learnt about the Golden Ratio in more detail, it was from a Murderous Maths book hehe.
For your problems/challenges, hehe are you listing people in each?
I thought you might want to put them so you can see people are trying these, do you think you could put me for your first one if this answer was right? blush I'm not concerned in the least bit with any glory or anything of the sort – just for whatever reason you wanted to list if you wanted to list people!
Sure! Sounds awesome! Yeah, I'll list people's creations!
I gtg, I've got a race tommorow.. need to sleep up for it
Ooh okay bye then, and good luck for tomorrow!!
Thanks! See you later
soo excited, I just quickly jotted down some random stuff
I love making diagrams so I made one just now!
Also (to anyone too) if I have any misunderstandings please feel very welcome to tell me e.g. I was thinking just now that the golden ratio is a ratio so is it
1.618... : 1 and is that separate to phi 1.618... itself, hmm
And now I just made another picture hehehe
Hey, @t1_hopscotch, would you like to make this more of a collab blog post? That might be a better idea, I'll change the title. Can't wait to start working
Ok, gtg. I'll be back to work on it tomorrow!
And okay goodbye for now!
I was thinking about what you said for making dots for triangle numbers, then I just did a quick picture
And woah I haven't ever really thought about polygonal numbers in general before! very cool!!
This is named Pascal's triangle in the western world after Blaise Pascal although it has been found earlier than him. (China used it hundreds of years before him)
Here are some quick pics:
Forming the triangle:
Patterns – the triangle numbers in one pair of the diagonals:
Patterns – the numbers in each row add to a corresponding power of 2:
(The sum of each row is double that of the last – this is effectively because each number in every row 'contributes' to two numbers in the row below it)
There are more patterns too
Video – thanks to @MR.GAM3R!
Can I add things to your post? You should add a link to the Numberphile video.
Yes! The more help, the better! I turned it on mass edit so have fun!
Yeah of course!! :DD Oooh I did not know that there was a Numberphile video on this, lemme find it.
Argh I had a whole post on the maths side of trig, from beginning – no prior knowledge required, but now it's lost in Help with code it would have been perfect for this topic...
Wish we could rescue the lost topics...
Haha it was a post that I spent a whole 2-3 hours on too
Oh! That's too bad
Why'd all the depreciated stuff get deleted. Bad bugs
Some other things about Pascal's Triangle that we should add
- Combinations, Permutations (then we could add something about factorials!)
- It has to do with powers of 11 where each row is a power of eleven. 11^0 = 1; 11^1 = 11; 11^2 = 121; 11^3 = 1331; 11^4 = 14641; then it gets strange, when you have a 2 digit number, you add the tens digit to the left section