saphi-maths

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I love that tensor product is just normal

mathermatical notation explained

symbol        meaning

=                   equals

=/=                not equals

<                   left

>                   right

!                    LOUD NUMBER

~                   worm

π                  stonehenge

√                   right answer

x                   wrong answer

⋯                  soon…

∮                   what Exacrly the fuck

∝                   fish

∞                   fish with 2 heads

↯                    lightning

:⇔                 he Scream

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it is forbidden

(multiply by a fraction instead)

Had a dream where they made division in mathematics illegal

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More specifically, the sum of cubes is exactly the square of the sum of integers up to the same number

1³ + 2³ + 3³ + 4³ = 100 = 10² = (1+2+3+4)²

1³ + 2³ + 3³ + 4³ + 5³ = 225 = 15² = (1+2+3+4+5)²

1³ + 2³ + 3³ + 4³ + 5³ + 6³ = 441 = 21² = (1+2+3+4+5+6)²

etc. :3

Hence √2025 = 1+2+3+4+5+6+7+8+9 = 9*10/2 = 45

not to be a number nerd on main but 2025 (45^2) will be the only square year most of us ever experience. the last one was 1936 and the next one will be 2116

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Integration between two curves

The purple areas are the same size before and after the transformation

I think they look pretty cool :P

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Polyhedron of the Day #212: Elongated pentagonal gyrocupolarotunda 

The elongated pentagonal gyrocupolarotunda is a Johnson solid (J41). It has 37 faces (15 triangles, 15 squares, 7 pentagons), 70 edges, and 35 vertices. Its Bowers-style acronym is epgycuro. It is constructed by elongating a pentagonal gyrocupolarotunda (i.e., inserting a decagonal prism between its halves). Its dual is not uniquely named.

Left image created by AndrewKepert using Cyp's povray macros, CC BY-SA 3.0, https://upload.wikimedia.org/wikipedia/commons/e/ef/Elongated_pentagonal_gyrocupolarotunda.png.

Right image created using Robert Webb's Stella software, found at https://www.software3d.com/Stella.php.

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Intro to Analysis

I've started studying real analysis over the summer since it is a class I will be taking next semester, and I am greatly enjoying it so far. I would like to share an interesting proof I read about.

The proof I am showing is that ℚ is dense in ℝ:

(a) x,y∈ℝ and x<y ⇒ ∃p∈ℚ such that x<p<y

Which means for every two real numbers x,y where x<y, you can always find a rational number between them.

To understand this proof, you need to know about the Archimedean property:

(b) x,y∈ℝ and x>0 ⇒ ∃n∈ℤ+ such that nx>y

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PROOF:

Since x<y, this implies that 0<y-x. By (b), we see that ∃n∈ℤ+ such that (1/n)<y-x, or that 1<n(y-x)=ny-nx.

When applying (b) again, we have that ∃m1,m2∈ℤ+ such that m1>nx and m2>-nx. Then, we get -m2<nx<m1.

We know that ∃m∈ℤ, where m2≤m≤m1, such that m-1≤nx<m.

Then, nx<m≤nx+1.

Since 1<ny-nx implies ny>nx+1, we have that nx<m≤nx+1<ny.

Since n>0, it follows that x<(m/n)<y.

This proves (a) for p=(m/n).

∎

Sources:

Rudin, Walter. Principles of Mathematical Analysis. 1953. 3rd ed., ‎McGraw-Hill Publishing Company.

The song I'm currently listening to:

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This reminds me of 6n ± 1

add 3 to "any" even power of 2 and you get a prime.

2+3? 5. prime

4+3? 7. prime

8+3? 11. prime

16+3? 19. prime

and it just keeps going

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yup, this exactly

people go "I hate maths" not realising that the thing they hate isn't even maths, so much as rote algorithms taught to them by a flawed education system

CanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtag

Can people stop putting math hate on the math tag ?????

pleaseeee like I just want to see some fun math stuff, a bunch of theorems and memes

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this

look, I don't need you to like maths, I don't need you to engage with things I talk about, but my lord, if I'm trying to talk about maths that interests me, and you walk in and shut me down with "oh, I hate maths" I am putting your head on a pike.

It's like me taking one of your favourite interests and going "I hate that thing specifically, stop talking about it" whenever you start to talk about it publically

Maths isn't this special kind of interest that people are allowed to hate on for no good reason

It's unironically alienating to be interested in maths, because people will just tell you to shut up when you're talking about it, something that people wouldn't do with most other interests.

CanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtagCanpeoplestopputtingmathhateonthemathtag

Can people stop putting math hate on the math tag ?????

pleaseeee like I just want to see some fun math stuff, a bunch of theorems and memes

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I love this immensely <3

fuck you unspinnable cube

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Statistics breakdown:

46.9% of responses to the first poll find "dude" to be gendered

52.8% of responses to the second poll find "dude" to be gendered

This implies there's a bit of a different demographic that is interacting with the second poll. I hypothesise that this is because transfems would be more likely to interact with the second poll, given it is targetted towards them.

Of transfems who answered the second poll, (26.3% of responses)

80.2% of transfems find "dude" to be a gendered term. 21.1 / 26.3 = 0.802

Of non transfems who answered the second poll, (73.7% of responses)

only 43% of non-transfems find "dude" to be a gendered term 31.7/73.7 = 0.430

We can conclude that, if you want to make transfems feel safer in spaces with and around you, that you should not use "dude" as a non-gendered term. Even ignoring the history of the term, and the misogynistic reasons behind why masculine terms have a tendency to become gender neutral, where feminine ones do so at a much lower tendency.

Do not use "dude" to refer to trans girls, thank you.

Bonus:

Although the last poll only has 25 responses, I figured I'd sift through it:

Yes (californian) - 3 votes Yes (not californian) - 14 votes No (californian) - 2 votes No (not californian) - 6 votes

60% of californian responses to this poll (which isn't very representative, given it is literally just 5 votes) find "dude" to be a gendered term.

compared to 70% of non-californian responses.

These numbers are closer to the transfem results of the second poll, thus I think the demographic that answered this poll likely is in larger part transfem.

You can't really conclude anything from this, since the sample size is too small.

Do you view the word "dude" as gendered?

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i was working on this funky problem

me when i bangle my isector

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me when i bangle my isector

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both the grammar and the maths check out :3

@saphi-maths opinions?

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If it helps at all, you can think of them by considering what happens in each:

Even functions:

Even functions can be written using exponents that are multiples of 2.

This means you can rearrange them into something like this:

Note the sideways looking M (it's a capital Sigma) just means "sum" here! It's because you can add any terms to make an even function:

g(x) = x⁴ is an even function, just as h(x) = x⁴ + 3x² + 2 is.

Since x² = (-x)². It doesn't matter whether x is positive or negative, the function will always give the same result.

And this is how we get f(-x) = f(x) for all even functions!

You can think of this as a line of symmetry along the y-axis! It doesn't matter what f(x) the value of f(-x) will always be the same.

Here's some gifs:

One that is simply f(x) = x²

And some more, funkier ones:

Note how this works even with negative powers!

To consider an example with actual numbers:

Odd functions:

Odd functions can be written using exponents that are one more or less than a multiple of 2.

Like with even functions, this can be rearranged, but into something more like this:

The first part is just like the even functions, but now we're multiplying it by x one more time.

This means that the sign of x does now matter. If x is positive, it will stay positive, if x is negative, it will be negative. That said, x and -x both have the same absolute size, so the end product will also still be the same size, just one would be positive, and the other negative.

Think how 2³ = 8 and (-2)³ = -8. Both have an absolute value of 8, just one is negative.

And so from this you get f(-x) = -f(x)

You can think of this as a rotation!

Here it is with x^3

Note how you can rotate it 180 degrees, and it ends up looking the same. This is basically what f(-x) = -f(x) entails!

Here's a couple more!

Note how like even functions, this also still works even with negative powers!

To give an example with numbers:

I hope this helps a little, If you have any questions feel free to ask ^w^

I probably didn't explain this particularly well, but I do hope this explains at least a little bit of the intuition between odd and even functions.

i hate even and odd functions