#math community

[xyymath]

Fun with Geometry: Shapes You Didn’t Know You Needed

Geometry is far more than the basic shapes we learn in high school; it’s a world brimming with bizarre and captivating figures that push the boundaries of our imagination.

1. The Hypercube (Tesseract)

The hypercube, or tesseract, is the 4-dimensional analog of the cube. While we live in a 3-dimensional world, the concept of a fourth dimension has fascinated mathematicians and artists alike. A hypercube consists of 16 vertices, 32 edges, and 24 square faces, each one being a 3D cube in a higher-dimensional space.

In the real world, hypercubes don’t physically exist, but they serve as key tools in higher-dimensional geometry and theoretical physics. Think of them as a "spatial metaphor" for the kinds of higher-dimensional spaces used in string theory or machine learning. Mathematicians use them to explore the complex relationships between different dimensions. The tesseract also shows up in pop culture, notably in the movie Interstellar, where it represents the connection between time and space.

2. The Pentagon (Not Just in Architecture)

The regular pentagon (five sides of equal length and five equal angles) has a fascinating relationship with the golden ratio. If you draw diagonals within a regular pentagon, they intersect in such a way that the ratio of the longer segment to the shorter segment is the golden ratio (ϕ ≈ 1.618). This means that pentagons are not just aesthetically pleasing in architecture, they have deep connections to mathematical beauty.

In nature, sunflowers and pine cones exhibit pentagonal symmetry. The arrangement of seeds in the flower follows a Fibonacci spiral, and the spirals are governed by golden angle, which closely ties to the pentagon’s unique proportions.

3. The Dodecahedron

A dodecahedron is a regular polyhedron made up of 12 pentagonal faces, 30 edges, and 20 vertices. It is one of Platonic solids, which means each face is identical, and the same number of faces meet at each vertex. This geometric shape is not just abstract; it appears in various 3D modeling applications and is used in architecture, like in the London 2012 Olympic torch design.

What’s particularly fascinating is its appearance in pop culture. The dodecahedron serves as a crucial symbol in the book and movie adaptation of The Hitchhiker's Guide to the Galaxy (the "Meaning of Life" puzzle) and is part of a well-loved mathematical riddle known as the "dodecahedron paradox."

4. The Möbius Strip

The Möbius strip is a non-orientable surface with only one side and one edge, and it is a staple of topological geometry. The twist in a Möbius strip turns the concept of inside and outside on its head. Take a strip of paper, give it a half twist, and then join the ends. The result is a surface where you can trace your finger along its edge endlessly, without ever lifting it or reaching a boundary.

Mathematically, the Möbius strip is a symbol of non-orientability and plays a crucial role in knot theory and the study of 3-manifolds. The Möbius strip also sneaks its way into art and architecture, often used as a visual symbol of infinity or paradox in both visual and sculptural art forms.

5. The Klein Bottle

Another topological marvel is the Klein bottle, a non-orientable surface with no boundary. Unlike the Möbius strip, which has only one side, the Klein bottle essentially has a single continuous surface where both sides are connected in a higher-dimensional space. If you attempted to build one in 3D, it would have to intersect itself. However, it can be imagined in 4-dimensional space.

The Klein bottle's properties make it a critical concept in topology, with applications in advanced physics and geometry, particularly when studying the shape of the universe and space-time curvature.

6. The Truncated Icosahedron (Football Shape)

Have you ever wondered about the shape of a soccer ball? It’s a truncated icosahedron. This polyhedron has 12 black pentagonal faces and 20 white hexagonal faces, a geometric structure that makes it easy to create spherical objects with flat faces. The truncated icosahedron is a close-packed shape and appears in carbon molecule structures such as buckyballs (or fullerenes) used in nanotechnology.

7. The Archimedean Solids

The Archimedean solids are a set of 13 convex polyhedra, where each face is a regular polygon and the same number of faces meet at each vertex. These shapes, such as the icosahedron (20 faces) and octahedron (8 faces), pop up in all kinds of real-world applications, like in architecture and crystallography. In fact, many molecular structures (like the shape of viruses) reflect these highly symmetrical solids.

Next time you look at a soccer ball, admire a piece of modern art, or even browse through a movie with some mind-bending geometry, remember: the world is built on shapes you never knew you needed, and math is at the heart of them all.

[kimblestudies]

would anyone be interested in an upper level mathematics discord? I know there's math and hw servers out there but I was thinking it may be nice to help each other with let's say everything past precal ?

[inkskinned]

you were raised in comparison.

it wasn't always obvious (well. except for the times that it was), but you internalized it young. you had to eat what you didn't like, other people are going hungry, and you should be grateful. you had to suck it up and walk on the twisted ankle, it wasn't broken, you were just being a baby. you were never actually suffering, people obviously had it worse than you did.

you had a roof over your head - imagine! with the way you behaved, with how you talked back to your parents? you're lucky they didn't kick you out on your ass. they had friends who had to deal with that. hell, you have friends who had to deal with that. and how dare you imply your father isn't there for you - just because he doesn't ever actually talk to you and just because he's completely emotionally checked out of your life doesn't mean you're not fucking lucky. think about your cousins, who don't even get to speak to their dad. so what if yours has a mean streak; is aggressive and rude. at least you have a father to be rude to you.

you really think you're hurting? you were raised in a home! you had access to clean water! you never so much as came close to experiencing a real problem. sure, okay. you have this "mental illness" thing, but teenagers are always depressed, right. it's a phase, you'll move on with your life.

what do you mean you feel burnt out at work. what do you mean you mean you never "formed healthy coping mechanisms?" we raised you better than that. you were supposed to just shoulder through things. to hold yourself to high expectations. "burning out" is for people with real jobs and real stress. burnout is for people who have sick kids and people who have high-paying jobs and people who are actually experiencing something difficult. recently you almost cried because you couldn't find your fucking car keys. you just have lost your sense of gratitude, and honestly, we're kind of hurt. we tell you we love you, isn't that enough? if you want us to stick around, you need to be better about proving it. you need to shut up about how your mental health is ruined.

it could be worse! what if you were actually experiencing executive dysfunction. if you were really actually sick, would you even be able to look at things on the internet about it? you just spend too much time on webMD. you just like to freak yourself out and feel like you belong to something. you just like playing the victim. this is always how you have been - you've always been so fucking dramatic. you have no idea how good you have it - you're too fucking sensitive.

you were like, maybe too good of a kid. unwilling to make a real fuss. and the whole time - the little points, the little validations - they went unnoticed. it isn't that you were looking for love, specifically - more like you'd just wanted any one person to actually listen. that was all you'd really need. you just needed to be witnessed. it wasn't that you couldn't withstand the burden, but you did want to know that anyone was watching. these days, you are so accustomed to the idea of comparison - you don't even think you belong in your own communities. someone always fits better than you do. you're always the outlier. they made these places safe, and then you go in, and you are just not... quite the same way that would actually-fit.

you watch the little white ocean of your numbness lap at your ankles. the tide has been coming in for a while, you need to do something about it. what you want to do is take a nap. what you want to do is develop some kind of time machine - it's not like you want your life to stop, not completely, but it would really nice if you could just get everything to freeze, just for a little while, just until you're finished resting. but at least you're not the worst you've been. at least you have anything. you're so fucking lucky. do you have any concept of the amount of global suffering?

a little ant dies at the side of your kitchen sink. you look at its strange chitinous body and think - if you could just somehow convince yourself it is enough, it will finally be enough and you can be happy. no changes will have to be made. you just need to remember what you could lose. what is still precious to you.

you can't stop staring at the ant. you could be an ant instead of a person, that is how lucky you are. it's just - you didn't know the name of the ant, did you. it's just - ants spend their whole life working, and never complain. never pull the car over to weep.

it's just - when it died, it curled up into a tight little ball.

something kind of uncomfortable: you do that when you sleep.

[queerism1969]

[cannibalisticdespair]

So, humanity is at over eight billion people. Time for a bit of statistics education for y'all, because I feel like it.

Okay, take a group that's around 1%. At least officially, it could possibly be higher. So like,

BPD: 1.6% officially

DID: 1.5% officially

Trans: 1.14% officially

Schizophrenia: 1.1%

These are American statistics, but presuming that overall none of these have some sort of strong cultural cause, they should be representative of the norm of humanity. Now, let's get the raw number estimate out of this. What we're going to need to do is multiply 8,000,000,000 by 0.016, 0.015, 0.0114, 0.011 respectively.

128,000,000

120,000,000

91,200,000

88,000,000

So, this a rough estimate for the number of people in each category respectively. Bit bigger than you might assume when you hear "approximately 1%", right? When you hear "approximately 1%", you're liable to think something is super rare. And in proportion, yeah, sure.

But plot twist, I'm discussing misinformation and bad propaganda. Did you know the internet allows disparate groups of small populations to connect and form larger communities than was ever possible offline due to how irl populations are distributed? Now, imagine a community of just 25% of trans people. Using the prior information, you can do this calculation yourself.

Done it? Did you get 22,800,000 people? Good job. If not, the calculation should have been 91,200,000 x 0.25. Now, imagine a community online of 22,800,000 people. That's a pretty damn big community online, right?

And this here shows how false claims of the level of visibility of various groups online being the result of "fakers" and "trenders" is. Those claims rely on your inability to understand that even 1% of humanity is 80,000,000 people. You aren't seeing anywhere close to 80,000,000 different people posting about it. You aren't even seeing 1,000,000 people posting about it. You are seeing a tiny fraction of a tiny fraction of humanity posting about it. Social media just enables that itty bitty bit to find each other and interact.

[purposeastro]

High Sex Drive| Vedic Astrology ( 18 + )

These Combinations and Aspects indicates a Higher Sexual Drive in a Person

If your Mars is in 1st 5th , 7th, 8th and 12th house aspected by Venus or in Venus Nakshatra then it gives native a very high sexual drive.

GEMINI MARS and SCORPIO MARS especially have higher sex drive.

GEMINI MARS aspected by Venus will get attracted to multiple partners and different types of sexual activities.

SCORPIO MARS is more on the hidden side deep and intense relationship with someone who noone knows.

MARS + VENUS in LIBRA and GEMINI shows Higher Sex Drive

RAHU + MARS in 5th House aspected by Venus

RAHU VENUS and MARS in 8th 7th or 12th houses can get agressive in sex and can harm themselves

This combination in 8th house with debilated planet can make the person into Rap*s, Extra Marital Affairs and Criminal activities.

MOON RAHU aspected by VENUS person will think about ssex sexual thoughts whole day. Involvement of Rahu will get into Porn. All the ONLY F@NS community and other things which are digital have Rahu energy in them.

VENUS SUN RAHU clearly shows extra marital and are mostly in prostitution and they can earn money alot due to VENUS SUN combination and rahu is online so through media.

Afflicted PISCES VENUS can make a person have higher sexual drive and more into these activities.

100 drops of blood = 1 drop of semen

1 drop of semen = 500 million to 700 million sperms and this is the nutrition for your brain as well.

Excessive masturbation can cause hair thinning, fuzzy vision and other issues as you're loosing your brains nutrition.

I'm doing Vedic Readings. Please Donate 👇👇👇🙏🙏

Radhey Radhey 🪷🪷🪔🪔🪷🪷

[anim-ttrpgs]

"Arithmomaniac," investigator Trait from Eureka: Investigative Urban Fantasy. Every investigator has 3 to 6 Traits!

[official-lucifers-child]

i’ve got my calculus III class today and i’m stupidly excited for it. the class is 75% full, run by one of the most chill professors (sent a welcome email that basically just said “hey don’t worry about anything ever. peace”), and also the most advanced calc class that the university offers.

[floralfractals]

so id say my tumblr network (as in, the people who tend to see/interact with my posts) is pretty mathy. i wanted to see how people interact w math and how they like to learn about it :) (and: maybe do something with that on my blog!!! wouldnt that be fun)

polls have a limited amount of characters i can add per option, so ill clarify some concepts here:

informal education is learning via a coordinated effort by an instance/expert outside of school system (e.g. voluntary lectures, social media posts, museum visits, youtube videos or similar). by informal i dont mean "its school but the teacher is chill" or independent research!!

formal education is learning through a school system (usually mandatory/with a teacher or professor present)

i refer to any education you do without making use of coordinated programmes as independent research, so that would be just you picking up an advanced math book to educate yourself, or perhaps scanning wikipedia, or emailing math profs with questions

when i talk about reading math in a general context, i mean that the material discusses math for a broad audience, so it doesnt talk about super niche specific mathematical concepts, and doesn't contain any complicated formulas/proofs/math speech

please do elaborate in the tags!!!

[divinit3a]

[xyymath]

Why the Number Zero Changed Everything

Zero: a concept so foundational to modern mathematics, science, and technology that we often forget it wasn’t always there. Its presence in our world today seems obvious, but its journey from controversial abstraction to indispensable tool has shaped entire civilizations.

1. The Birth of Zero: A Revolutionary Idea

The concept of zero didn't exist in many ancient cultures. For example, the Greeks, despite their advancements in geometry and number theory, rejected the idea of a placeholder for nothingness. The Babylonians had a placeholder symbol (a space or two slashes) for zero, but they didn't treat it as a number. It wasn't until Indian mathematicians in the 5th century, like Brahmagupta, that zero was truly conceptualized and treated as a number with its own properties.

Zero was initially used as a place-holder in the decimal system, but soon evolved into a full-fledged number with mathematical properties, marking a huge leap in human cognition.

2. The Birth of Algebra

Imagine trying to solve equations like x + 5 = 0 without zero. With zero, algebra becomes solvable, opening up entire fields of study. Before zero’s arrival, solving equations involving unknowns was rudimentary, relying on geometric methods. The Indian mathematician Brahmagupta (again) was one of the first to establish rules for zero in algebraic operations, such as:

x + 0 = x (additive identity)

x × 0 = 0 (multiplicative property)

These properties allowed algebra to evolve into a system of abstract thought rather than just arithmetic, transforming the ways we understand equations, functions, and polynomials.

3. Calculus and Zero: A Relationship Built on Limits

Without zero, the foundation of calculus—limits, derivatives, and integrals—wouldn’t exist. The limit concept is intrinsically tied to approaching zero as a boundary. In differentiation, the derivative of a function f(x) is defined as:

f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}

This limit process hinges on the ability to manipulate and conceptualize zero in infinitesimal quantities. Similarly, integrals, which form the backbone of area under curves and summation of continuous data, rely on summing infinitely small quantities—essentially working with zero.

Without the concept of zero, we wouldn’t have the means to rigorously define rates of change or accumulation, effectively stalling physics, engineering, and economics.

4. Zero and the Concept of Nothingness: The Philosophical Impact

Zero is more than just a number; it’s an idea that forces us to confront nothingness. Its acceptance was met with philosophical resistance in ancient times. How could "nothing" be real? How could nothing be useful in equations? But once mathematicians recognized zero as a number in its own right, it transformed entire philosophical discussions. It even challenged ideas in theology (e.g., the nature of creation and void).

In set theory, zero is the size of the empty set—the set that contains no elements. But without zero, there would be no way to express or manipulate sets of nothing. Thus, zero's philosophical acceptance paved the way for advanced theories in logic and mathematical foundations.

5. The Computing Revolution: Zero as a Binary Foundation

Fast forward to today. Every piece of digital technology—from computers to smartphones—relies on binary systems: sequences of 1s and 0s. These two digits are the fundamental building blocks of computer operations. The idea of Boolean algebra, where values are either true (1) or false (0), is deeply rooted in zero’s ability to represent "nothing" or "off."

The computational world relies on logical gates, where zero is interpreted as false, allowing us to build anything from a basic calculator to the complex AI systems that drive modern technology. Zero, in this context, is as important as one—and it's been essential in shaping the digital age.

6. Zero and Its Role in Modern Fields

In modern fields like physics and economics, zero plays a crucial role in explaining natural phenomena and building theories. For instance:

In physics, zero-point energy (the lowest possible energy state) describes phenomena in quantum mechanics and cosmology.

In economics, zero is the reference point for economic equilibrium, and the concept of "breaking even" relies on zero profit/loss.

Zero allows us to make sense of the world, whether we’re measuring the empty vacuum of space or examining the marginal cost of producing one more unit in economics.

7. The Mathematical Utility of Zero

Zero is essential in defining negative numbers. Without zero as the boundary between positive and negative values, our number system would collapse. The number line itself relies on zero as the anchor point, dividing positive and negative values. Vector spaces, a fundamental structure in linear algebra, depend on the concept of a zero vector as the additive identity.

The coordinate system and graphs we use to model data in statistics, geometry, and trigonometry would not function as we know them today. Without zero, there could be no Cartesian plane, and concepts like distance, midpoint, and slope would be incoherent.

[study-diaries]

Math Tips

(Pictures are not mine)

Well, let me tell you, we all have this love-hate relationship with this subject, right? The worst part is that when you don't know what the heck is going on, so, as a girl who studied maths (2 Volumes/textbooks) on her own during the year she was homeschooled, here are some tips and tricks that I did to get an A+ in my math finals!

Get your syllabus together

In the beginning I had no damn idea what was going on and it was just confusing. I had to do the first thing I did was taken my index/table of contents and mark the chapters which i knew very well and the ones I had no clue about. And then i arranged them with the marking scheme, like which one carries the most marks etc etc and study accordingly.

Complete lessons/chapters that you already know

When you finish off the things you already know then that's gonna give you the confidence you need even if you know only 1-2 chapters, learn it throughout and make sure that you'll get the answer no matter how twisted the sum is. If you're doubtful about the whole textbook like any normal person.... Start with the easy ones. (I know there are literally really no "easy" chapters, spare me)

Harder chapters need hard work

Most chapters like Trigonometry proofs, Geometry proofs, Algebra, Graphs, Mensuration and Calculus etc need more than minimum effort but here's a trick, what is the common thing in this? Yes, they're all formulae and theorem based which goes to my next point. These chapters are completely based on how much you've understood your basics.

Formulae and theorem cheatsheets

Make a list of all formulae and the theorem used in the book, write them chapter wise and no printouts or digital notes. Take a paper and write it down, no excuses. It helps you while you're practicing, revising and in the last minute review, it helped me damn much. Remember, maths is a sport. The basic formulae must come to you like reflexes.

YouTube is your best friend.

For every single chapter, go and watch the basics and how a sum is done step by step. A recommendation for this is Organic Chemistry Tutor who literally is one of the reasons i passed. He has videos from basic geometry, trigonometry, statistics to calculus. Search for your own YouTubers and be clear with concepts.

Math is fully memorization

Memorize formulae and theorems with the back of your hand, you should be able to recall them within seconds. Be thorough.

Memorize basic math values (if calculator isn't allowed)

Do this if you have a majority of chapters like Statistics, Mensuration, Profit/loss calculation etc, where large numbers are concerned. Memorize the first 10 square, cube, decimal and multiplication values. It may be dry but there are literally songs available for these things, I'm serious, i learnt the first 10 cube roots by listening to Senorita xD Search for rhymes and they'll definitely be many!!

Work it out!!!!!!

Can't stress this enough, atleast 30-40 mins is the minimum for maths. I'm serious, work out each sum, don't ever think it's a waste, you'll see the results. Practice makes perfect. Work out every single sum, from examples to exercise ones cause let's be honest, our examiners love to take problems from every nook and cranny of the book.

Whiteboard method

So, I made this up and it actually works, if you have a whiteboard or anything else, once you completed a chapter, take a random page and whatever sums you have on those two pages, you need to complete within a given time limit. It helps you to identify your weak points and where the hell you're losing both time and effort and not to mention that it gives you confidence boost up.

Hope this helps :))

[egotisticaleaderr]

Drawing two struggling at doing basic math question bc I hate math

[septune13]

its pathetic businessman griffith’s crush: former construction worker, current engineering student, himbo guts

[scp049swifey]

I made this little doodle of the doctor in math class because I was bored

[purposeastro]

7th house Secrets Vedic Astrology Part 2

7th Lord in 1st House

The person will get changed after marriage. 7th house is the house of perception in Vedic astrology. How you look outwardly and how people see you. Your public image. So the person will change according to people. The person will not think about how they're feeling they'll think about how the public is feeling after seeing them. So here the spouse will help to make you good or make you worse. For this you need to check many factors in the birth chart. Spouse will be DOMINATING. As 7th Lord your spouse is in 1st house which is your own house so you may lose your own personality with this. The person may start fearing public or spouse to make changes and adjust. The person get support from the spouse family, will see gains in money and personality development after Marriage.

7th Lord in 2nd House

The 2nd house in Vedic Astrology is related to Food therefore after marriage the person will have major food habit changes, the person will gain resources, If that's a malefic planet then maybe the person will get smoke habits from spouse even the the person doesn't smoke in their life but from spouse influence the person will start doing smoking, alcohol, etc. The person will definitely get rich after marriage but there'll be not so good relationship with in laws and fights can happen.

7th Lord in 3rd House

The 3rd house in Vedic astrology is your inner self it shows your deepest darkest fantasies. The people who goes against the norms our LGBTQ community peeps 👋💕 This is the combination in most of the LGBTQ community and they go against the norms by liking and doing things for the people of Same gender, etc. They can even changed their own religion ( if any ) for their spouse. Their behaviour changes after marriage. This is also an indication of Divorce if there's no good aspect here. So marry after getting your subconscious mind cleared and your subconscious, religion, etc. should match with the other persons otherwise chances of divorce will get stronger.

7th Lord in 4th house

The spouse will be very nurturing, caring. The person's basic values will change after marriage. The career will rise will get alot of money and property. The spouse will have huge impact on the person's karma and future upbringing by imbibing good values to you. You'll have to unlearn and learn things from your spouse. The person location may change or have to change the vaastu of the house. Again any malefic aspects can make the things bad and can lead to divorce.

7th Lord in 5th House

The 5th house in Vedic astrology is your (purva punya) Past life good karmas and now you're connected to your past life therefore you'll have less freewill. But this indicates love marriage as you are now connected to your past life karmas.

7th Lord in 6th house

The 6th house in Vedic Astrology is of Disease, Debts and Enemies therefore this too is not considered good combination but if this combination is in positive then the spouse will help to take you out from all these things which denotes the 6th house. But after marriage Disease, Debt and Enemies will increase so it's not so good Remedies are required.

7th Lord in 7th house

The 7th Lord in 7th house looks and sounds so good but in reality it's a negative Placement. The spouse will be strong, dominating and the spouse family will have better condition from the person's own family conditions. The person will get status and their life will start to change but the spouse will be so dominating that the person might not be able to endure their dominance which can start ego clashes and fighting. You'll feel powerful cause of your spouse and their status. The spouse will be better looking than the person or native, better working position, more money than the native.

7th lord in 8th house

The 8th house is the house of suddenness in Vedic astrology therefore spouse may suddenly get into health problems with this placement. The person may suddenly get into financial issues due to this and the person themselves can suddenly get sick. So if this is in positive then the person will suddenly get money 💰 So this is mixed combination as you can see. The spouse family will be stronger and wealthy and may help the person out when this combination is positive if negative the person may get into disputes with in laws. This can also creates No marriage or Sanyaas to the person. Remedies are needed.

7th Lord in 10th House

The spouse may be in your office, or have same career field, or on your floor where you are working. Good for Office Romance 💒 The person and the spouse will have Same mindset and similarities and will have work life balance. You can do partnership businesses with your spouse. You may fight with your spouse due to competitiveness so the ego will create fights.

NOTE : Please don't feel depressed or Sad as there are many things to take into account and no placement is bad placement NOT GOOD doesn't mean BAD. Your Birth Chart is just a GUIDE MAP and you can still choose whatever path you want with your willpower and GOOD KARMA guys always remember AHAM BRAHMASMI 🥹 I'M DIVINE OKAY! :) 🫶

I'm doing Vedic Readings. Please Donate 👇👇👇🙏🙏

Radhey Radhey 🪷🪷🪷🪔🪔