TimMathsNerd

As I appear to be gaining a number of followers every day, I feel like I should introduce myself a bit more than my bio. My name is Tim, I'm a mathematics student (just finished my 1st year of my undergrad). 1/

Idk if that answers your question but it's the best I can do. It may just be beyond my scope, though I have no way of knowing if it is or not.

You'd have a hard time expressing any number that isn't a sum of powers of pi in this base, in fact I'm not sure how possible it would be to do. I don't know how useful such a thing would be besides discussions about the philosophy of nominalism in maths.

Taking pi as the base for a counting system doesn't change any of the properties of the number. In the same way that 10 in decimal is the same as 101 in turnary, you can write pi in decimal is the same as 1 in base-pi.

The fun thing about transcendental numbers is that not only can they not be written in integers, they cannot be expressed using standard arithmetic. sqrt(2) is just sqrt(2), i is just sqrt(-1) but there is no such expression for pi.

Unsure what the question is. Also, I may be going into differential geometry now. Things are up in the air atm :P

Ooooo, this one was good. My proof touches on combinatorics and group theory/set theory. I also kinda stumbled onto the answer for n distinct beads though I didn't prove the statement, only asserted it. I hope you guys will be able to read my handwriting

The best kind of compliment, thank you :)

Apologies for the crappy handwriting😅

Not sure what you mean by "sidestepped n=3"? Also, thanks 😊

There's controversy around whether the day should be held, or whether the official event/thing that is celebrated should be changed. However, as previously stated, most people just use it as an excuse to get off work and have a good time with friends and family.

Australia Day is, ostensibly, a day every year where folks celebrate the arrival of the British at Port Jackson and the raising of the flag of Great Britain. These days, most people don't know what the day actually celebrates and so celebrate 'being Australian' instead.

Hahaha, I got that too! I wonder why...

For our puzzle n=16 and r=8, so plugging those values into the aforementioned formula gives us (16x15x14x13x12x11x10x9x8x7x6x5x4x3x2x1)/(8x7x6x5x4x3x2x1) Which can be tidied up into 16x15x14x13x12x11x10x9 Which equals 518,918,400.

In the notation it's written as "nPr", where n is the number of objects to choose from and r is the number of objects we need to choose. The formula to calculate this is n!/(n-r)!.

We continue this process until we have accounted for all 8 squares we need to place. This process has a name in combinatorics: finding the number of *permutations* of a given set.

We first notice that the large square is made up of 16 smaller squares and so half of it is 8 squares. If we had a blank 4x4 grid, we have 16 places to choose to put the first square. We then have 15 places to choose to put the 2nd square because the first square takes one place.