I was trying to prove the Pythagorean theorem on my own and stumbled into this.

You take a right triangle and create three similar triangles by scaling each one by one of the side lengths and rearrange them into a rectangle with one side being a^2 + b^2 and the opposite side being c^2 so a^2 + b^2 = c^2.

If you wanted to, you could use the two smaller triangles in the diagram in a different arrangement to form the larger triangle, but I like the way it looks in a rectangle more.

I showed it to a professor and he encouraged me to publish it. I’m thinking I will. I really like this proof and I want to show it to people.

I couldn’t find an example of this proof anywhere. I came across some that looked similar but they seemed to use different logic. I figured I’d try to publish this, but I’m not really sure how to.

I’m not well versed in the community around sharing math and I’m not sure what is seen as worth sharing. Does anyone got any advice on how I can share something like this?

Also, does this count as a proof? Were there any assumptions that need to be explained or does this stand on its own?

I didn’t really explain how they come together to form a rectangle but I’m not sure whether or not it’s a big enough leap that it should be explicitly stated.

I have a young teen that is experimenting with math and the Desmos graphing calculator. These are his questions, which admittedly is beyond my math knowledge. Any tips or resources are appreciated!!

Is there any way using the most generalized way of defining operations so that any line or equation or function has an imaginary aspect to
It?

If so, is there a way it will always have that index?

If the index were to approach infinity, would the graph create a shape that looks like a 3d object?

Is there a way to predict what the imaginary part will look like and manipulate what it would look like on the graph?

https://royalsocietypublishing.org/rsta/article/378/2163/20180437/111559/Living-with-Ramanujan-for-40-yearsLiving-with

So apparently within a few months(or some would even argue a few years) there has been a drastic change in the posts being made in this sub leading to almost total erasure of different kinds of posts. What is the one that you miss the most.

Also any other changes observed,thoughts are also welcomed :), feel free to share!

Today I've published the beginning of the end, for my private exploration of following the root of a value till one or below, at 16 bits.

I do not formally know all the usages of such a value, or components'.

I've made it publicly accessible and licensed for usage and protection.
Please feel free to explore into it yourself.

Language and calculations run via python, with some functions used to help as a base default.

Welcome to the unknown, are you scared?

~ Iroh

[ 0.3134313340312133643109333280398413295243... ]

Programmed Blender 3d to Generate this one. Thought it turned out pretty well.

Mine is probably Hodge structure of motivic or representation theoritic objects. I know it's essential and extremely important and stuff. But I just can't see the beauty in it.

I need it all the times and its presence matters enormously. Sometimes I work with PEL Shimura varieties just to avoid having to deal with the Hodge questions. I couldn't escape it though this time as Hodge structure provides a controls the behavior of L-functions at infinite places.

I know the traditional way to define complex numbers is to start with real numbers and then define complex numbers as ordered pairs of real numbers with certain algebraic properties.

I wanted to ask if there is a way to define complex numbers without reference to real numbers. What I have in mind is a set of axioms for complex numbers which would would define them as a kind of field. Like real numbers are often axiomatized as a complete ordered field. Does such axioms exist?

Please note that I do not, at this moment, posses any significant knowledge of abstract algebra or any other higher mathematics, beyond say hearing about the names of some things.

I know there’s probably a good reason, but I thought this is what LEAN was made for?

Hi everyone!

I’ve been using physical pocket calculators since the mid-1980s, and I’ve always loved the speed, tactile feedback, and direct control of hardware key layouts. The main motivation behind ViCalc was to bring that exact same speed and workflow efficiency to a modern PC keyboard—allowing you to touch-type mathematics seamlessly without taking your hands off the keys to click UI buttons.

Rather than just imitating a physical handheld calculator, ViCalc is built to optimize desktop mathematical workflows and complex calculation tracking.

🧮 Key Features & Workflow Design

• Direct Keyboard Mapping: All functions and operations are directly mapped to your PC keyboard, eliminating the need to click through UI buttons with a mouse (though mouse/touch interaction is fully supported if preferred!).
• Full & Exportable Calculation History: The entire step-by-step history is logged automatically as you work. This makes it effortless to review your process or copy-paste the entire multi-step calculation directly into research notes, LaTeX documents, or technical reports.
• Flexible & Adaptable GUI:
  • Minimalist View: Hide virtual keys entirely—ideal once you learn the shortcut mappings by heart.
  • Custom Views: Toggle between a standard numpad, a compact left-side layout, or a full scientific keyboard layout.
  • Expandable History Pane: Easily track, review, and manage long sequence calculations.

🛠️ Modes & Technical Details

• Scientific & Complex Modes: Full suite of trigonometric, scientific functions, and complex arithmetic support.
• Programmer Mode (Base-N): Bitwise operations and conversions across Hex, Dec, Oct, and Bin.
• Language: Python 3
• License: Open Source (MIT License)

🔗 Links & Downloads

• GitHub Repository: github.com/Kudaschov/ViCalc
• Windows Installer: ViCalcSetup.exe
• Homepage: kudaschov.de/en/vicalc-4

I’d love to hear your thoughts, feedback, or any feature requests from the community! How do you currently handle rapid calculations and history logging on desktop?

As the title states. What else is it usefull. Thanks in advance

Was just reading on landing gears out of interest, (engineering undergrad) This is how a gear retracts inside (to increase aerodynamics)

The second one is an example of space saving, the drawback is less clearance & clashing. Now suppose I try to form mathematical modelling eq of the trajectory to describe the geometry such that clashing is avoided (in case of turbulence) and we need to fix some clearance..... How would you approach this ? What field of maths am I vaguely thinking about ?

I would just like some general advice about pursuing a mathematics PhD. My applications will be for mainly applied mathematics programs, or something with computing. I currently have a 4.0 in a Math/Stats major ( may drop a little though after this semester ), a REU, poster presentation and a talk, potentially an upcoming internship at SULI for the spring, and I would like to think 2 pretty strong recommendations ( one from REU, one from Real Analysis where I got an A+ and he’s a well-respected professor ). The advice everywhere is to apply for safety schools with lower national ratings, some matches, and a few stretches. I was advised to apply to 12-20 schools. I’m unsure which schools are truly safeties or matches, because some lower ranked schools only accept 5 new students so I wouldn’t truly consider that a safety. Any tips or advice?

Transferred from a community college with As in everything up until calc 3 and differential equations.

First term and I’m taking proof and logic and a proof based linear algebra course(and probability theory but it’s been easy thus far) and I’m debating if this is for me.

I genuinely enjoy math, and have systemized my way of studying it but I feel like I’m not yet accustomed to the jump from computational to proof based mathematics

Do I just accept my B/C’s? Will that affect my graduate/postgraduate applications and what if I retake the class?

I’d be appreciative of any and all tips.

We take a point and give it a function f(x)=x^2, so 1=1, 2=4, 3=9 and so on. Now, as we have given the point function, it is changing, or in physics terms, the point experience excitation. Which brings me to my point, the number is being tempered with so, does it change the nature of the point, could the point not really be a point but a sphere that experiences rotation on disturbing it with a new function.

So maybe 2^2 = 4 and -2^2 = 4 but the rotation of the point, say along the z plane is saying +90° and -90° or vice versa, but is in a confined space of real number (why confined, explained later), as it is a point, so just a rotation and not movement.

Adding a bit of physics to it - Maybe not a rotation but concentration of energy in the confined space of the real number of unit 1 or x, or say |1/12|.

P.s. I think of it because I see Remimann hypothesis and see that the number along 1/2 plane contain complex numbers and so they might contain a rotation as well. The results are not along a line of 1/2 but along a plane of 1/2, with confined limits to the z plane.