/r/CasualMath

This is a subreddit that is meant to be somewhere inbetween /r/math and /r/learnmath.

This is a subreddit that is meant to be somewhere inbetween /r/math and /r/learnmath.

It is my hope that crummy mathematicians can discuss old ideas and prove old theorems and solve old puzzles here. Just because someone did it before doesn't mean we can't have fun with it, right?

This is a place where things like the Ulam Spiral and prime-rich polynomials are tolerated as reposts.

Please do use freely available resources where possible. Some crummy mathematicians aren't as fortunate as you are :)

This is our wiki and we encourage contributions of any sort, especially if they're interesting.

Post Spoilers in this format
`[X proves Y!](/spoiler)`

It will show up like this:

X proves Y!

**Using LaTeX**

To view LaTeX on reddit, install *one* of the following:

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TeXtheWorld Greasemonkey userscript

`[; e^{\pi i} + 1 = 0 ;]`

Post the equation above like this:

`**[**; e^{\pi i} + 1 = 0 ;**]**`

You may need to add four spaces before or put backticks around math fragments.

**Using Superscripts and Subscripts**

x*_sub_* makes x*sub*

x*`sup`* and x^(sup) both make x^{sup}

x*_sub_`sup`* makes x*sub*`sup`

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/r/CasualMath

3

Well after solving a little bit we will arrive at

(y^2-x^2)/(x-y) = (y^2-x^2)/(x-y)

and then as in title doing cross multiply hence the ans 1? Is this ans valid or am I doing something wrong

4 Comments

2024/06/29

11:04 UTC

11:04 UTC

1

0 Comments

2024/06/28

12:16 UTC

12:16 UTC

5

https://youtu.be/xGxSTzaID3k?si=HmfD7IUxm_pKsFab That's a pretty interesting topic for a presentation I want to give in school. The problem is: I don't quite get it. I understand everything before and after minute 14:36 but I just don't get why the speeds are equal and what this has to do with the stationary rim property. I would be very grateful for any help!

1 Comment

2024/06/27

19:18 UTC

19:18 UTC

1

0 Comments

2024/06/24

12:47 UTC

12:47 UTC

0

At least once a year social media is plagued with people arguing over the answer to a simple math problem, and it's almost always because these memory aids don't work. People end up misremembering the order of operations because of the memory aid that is supposed to help them. The number one issue being people thinking there are 6 steps in the order operations when the are 4. You multiply and divide together, and you add and subtract together.

The annoying thing is I've seen math phds mess this one up. Granted, after about algebra 2 you are not going to be using "÷" anymore because it's too limiting, so they are waaaaayyy out of practice.

My point is, we need new memory aids, these ones aren't working.

5 Comments

2024/06/21

17:40 UTC

17:40 UTC

5

Consider the equation:

x^2 + 1/x^2 = a

This problem is usually solved by simplifying it to

y + 1/y = a => y^2 -ay + 1 = 0

And then y = ( a +/- sqrt(a^2 - 4) )/2

So, x = +/- sqrt(y) = +/- sqrt((a +/- sqrt(a^2 - 4))/2)

However, I tried solving this using complex numbers under the assumption that all real numbers are complex numbers. I immediately hit a roadblock trying to represent a real number in terms of re^(iθ). Because then the real number is r and θ = 0. However, here's the trick:

Since z = re^(iθ), and r = e^( ln r ), we have:

z = re^(iθ) = e^( ln r ) × e^( iθ ) = e^( ln r + iθ )

Thus, z = e^( z' ), where z' = ln(r) + iθ

With this transformation, we can represent x (assuming it is a complex number) as e^z such that z = ln(r) + iθ and x = re^(iθ). Now,

x^2 + 1/x^2 = e^(2z) + e^(-2z) = 2cosh(2z)

Therefore,

a = 2cosh(2z)

a = 2cosh( 2ln(x) ) [Since x = e^z , z = ln(x)]

And so, 2ln(x) = arccosh(a/2)

x = sqrt( e^(arccosh a/2 ) )

I never thought such an analytical solution would be possible. This is a neat solution with familiar mathematical functions instead of taking square root of square roots. This is what I consider a beautiful solution.

1 Comment

2024/06/21

15:19 UTC

15:19 UTC

5

We call square numbers "square" because they can be arranged into squares geometrically.

Given this, I'm surprised we don't call composite numbers "rectangle" numbers

15 Comments

2024/06/19

00:54 UTC

00:54 UTC

4

I know it's a stupid question and the answer is 99% no but I'll ask anyway.

I have four possible answers. At least one of them is correct (meaning there can be two or even three correct answers), however we're not told how many answers are correct in the question.

I get +1 point for a correct answer, and -0.5 points for giving an incorrect answer. No points for giving no answer (not choosing the correct answer is not penalised).

Does it make sense to guess here? If I don't know the answer, can I maybe click on two answers since if I get only one correct I will still get +0.5 points?

1 Comment

2024/06/18

14:15 UTC

14:15 UTC

1

0 Comments

2024/06/18

13:06 UTC

13:06 UTC

2

0 Comments

2024/06/17

02:52 UTC

02:52 UTC

4

I have been using photomath pro for my A-levels and its best, now i am worried at advanced Linear or abstract algebra or calculus 2, 3 what app will i refer for step by step solution so i can self study hard. I am kinda worried also out prof. notes are kinda shit and isnt damn interested in question out of his syllabus, please recommend me anything you can would be helpful.

1 Comment

2024/06/14

04:27 UTC

04:27 UTC

4

So i just learned about this Problem, if you dont know what it is Search it up. I was very sure it was 50/50, but After thinking a day, i found this: So the Chance that you Picked at the beginning a goat is 2/3. Chance for the Car is 1/3. if you First Choose the goat(which Happens 2/3 of the Time), the moderator Needs to pick the other goat door, so there is the 2/3 Chance that the Last door is the Car door. So thats the proof, for questions ask me, im sorry for my english, im german and Auto correction fucks everything up

:)

1 Comment

2024/06/13

21:18 UTC

21:18 UTC

10

Well, let's ask Microsoft Copilot (based on OpenAI/GPT-4):

9 Comments

2024/06/12

09:14 UTC

09:14 UTC

2

Hey Everyone,

Not sure if this is allowed here, so please delete if not, but I just wanted to share a Math game we created called SolveSum. Figured this community might enjoy a new puzzling math game to play as much as we did playing and making it!

The game is a tile swap game mixed with the likes of Sudoku and is great for building addition skills and learning!

Essentially you swap tiles to make the row or column collection of tiles add up to the row/column header, and if you are successful you gain a point. You can change the size of the grid to make it more difficult or easier, and are allowed 3 shuffles per game. Get as many sums solved to grow your score!

Check it out! SolveSum, is on both Apple App Store and Google Play! Cost: $0.99

0 Comments

2024/06/09

00:08 UTC

00:08 UTC

4

I am studying for a math test, that will determine the math class I get for college, I was never a big fan of math (I blame my teachers) so I only ever worked hard in math two of the twelve years in school. The test will go over Algebra, Geometry, and Statistics. I would like any suggestions about ways to remember formulas or free websites that could assist me in studying.

1 Comment

2024/06/05

23:05 UTC

23:05 UTC