If A Homomorphism Is A Structure Preserving Map And An Isomorphism Is A Bijective Homorphism, Does That

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Reload it and immediately turn off your Internet access (data/WiFi if you are using a phone)

Reload it and click the 'X' next to the return icon on the top left of your window (if you are on desktop)

Reload the page, type 'Ctrl+ A' and 'Ctrl+ C' and paste everything onto an open document

this has worked for me 97ish % everytime hope this works for u too

Pick a point inside a triangle and drop perpendicular projections onto the sides. These define another triangle. Repeat, with the same point but within the new triangle. Do the same thing once more. The fourth triangle now has the same angles as the first one, although it’s much smaller and it’s rotated.

6 Things People Don't Always Tell You About Studying

1. you ace tests by overlearning. you should know your notes/flashcards/definitions basically by heart. if someone asks you about a topic when you’re away from class or your notes and you can answer them in a thorough and and accurate answer, then you’re good, you know the material. 

2. if you don’t understand something, it will end up on the test. so just don’t disregard and hope that this specific topic won’t be on the test. give it more attention, help, and practice. find a packet of problems on that one concept and don’t stop until you finish it and know it the best. 

3. sometimes you just need that Parental Push. you know in elementary school, they would tell you “ok now it’s time for you to do your homework! you have a project coming up, start looking for a topic now!” ONE of your teachers might be like this. be thankful for it and follow their advice! these teachers are the best at always keeping you on track with their calendar. if not a teacher, then have one of your friends be that person that can keep you accountable for the things you promised you would do. 

4. you just need to kick your own ass. seriously. i know it sucks and its hard to study for two things at once. BUT. I DONT CARE IF IT’S HARD. you need to do it and at least do it to get it over with because you can’t keep putting things off. If you do, you will eventually run out of time and you will hate yourself. force yourself to do it. i made myself sign up for june ACT even though there’s finals because if i didn’t, i probably never would. like do i think i’m gonna be ready in one month? probably not, SO I BETTER GET ON IT AND START STUDYING! 

5. do homework even if it doesn’t count. if you actually try on it, then you will actually do so much better on the tests, it’s like magic. 

6. literally just get so angry about procrastinating that you make yourself start that assignment. I know how hard it is to kick the procrastination habit. I have to procrastinate. So I make myself start by thinking about my deadlines way early. I think, “oh i have a presentation in three weeks (but it really takes 2 weeks to do), i’ll be good and start today.” when that doesn’t happen, you say you’ll do it tomorrow, and this happens for like the next four days. I get so mad at myself for not starting when i am given a new chance to do so with every passing day. By that time, you actually have exactly how much time you need for it AND you were able to procrastinate the same way you usually do ;)

Lagrange Markipliers or something idk I forgot all my multivariable calc.

also i'm having a quarrel with my parents, i'm afraid they will disown me or kick me out

they are anti-vax and full-blown conspiracy theorist and my mother found out i took a covid vax

the fact that my father believes the earth is flat makes me so motivated to become a full-time scientist, being the very thing they hate. then they could not undermine what i say with "what the fuck do you know, you're just a student"

my father likes you only if you agree with him and he literally tells me every time we talk that i am stupid and should go fuck myself. not that i don't say the same things to him, i do, i hate the fact that this is how this relationship works

i am aware that doing things to prove something to someone is not the way to go but up to this point it was just my goal, one of many, to be a scientist, now it feels like a necessity

Complex Number Grapher

https://jutanium.github.io/ComplexNumberGrapher/

This grapher is really fun to play around with! 

A normal function takes in a number, x, and outputs another number, y. But a complex function takes in a complex point on a plane (a+bi) and outputs another complex point. Without 4 dimensions, it would be impossible to graph a complex function :(

The creator of this project instead uses complex domain coloring which they explain much better than I have here so you should 100% go and check it out!

Look at this cool function I got:

f(z)=(sin(z^3))^((cos(z))/2)

A monoid? Oh, you mean a monad on a one point set in the bicategory of spans of sets?

What's the beef between engineers and physicists and even mathematicians.

Why physicists mock mathematicians: Because playing 51 dimensional chess against your own brain seems silly to us when there’s a whole cosmos to explore.

Why mathematicians mock physicists: The universe can only be understood because some nerd spent the time playing 51 dimensional chess and in the process they created some useful stuff for the physicists to steal and abuse the hell out of.

Why everyone mocks the engineers: π=e=3 is an abomination before God and those pencil pushing dorks make more money than us so we feel the need to vindicate our $75000 student debt.

Square is a rhombus, regular hexagon can be tessellated with three equal rhombuses, and every regular polygon with even number of sides can be rhombi-tessellated.