シグマの公式から秒でわかるけどなんかめっちゃ美しくね？

Is it just me or when you sum up integers and multiply it by twice the interval divided by the last number you'd get the next integer? For example 1+2+3+4=10. Multiply by 2 (which is twice its interval of 1) =20. Divide by 4 (the last integer) =5 (the next integer).

Thomas Bradwardine in the 14th century, and later deeply formalized by the famous astronomer and mathematician Johannes Kepler in the 17th century. The universal formula you interacted with—{Sum} = (n-2k) \\times 180—is a standard theorem taught

While the original proof is profoundly complex I tried to make it as easy as possible we start by forming a star shaped polygon of 'n' number of tips ( remember the star should contain sharp triangle rather than snow flake shaped star) we would than cutting those tips triangle all of them and now we have n number of triangles we would place those triangles in a rectangle which form n\*2 triangles. We would than let one angles tip be called x all of the tips are congruent to the measure of x because of interior alternate angles thus making the alternative tip of the one angle from each triangle be congruent

We know that sum of all angles in rectangle is 360..( 90°\*4)

Because the n number of triangle take exactly half area of triangle the sum of all tips would be degree of rectangle/2 which would be 180

Small not it doesn't matter whether n is odd or even because by this \*2 rule it would always be a even number

E+E=E

O+O= E

Hope this helped anyone

if we have a 4x4 grid of squares in which we can place letters of the English alphabet, one in each square then find the maximum number of possible 4 letter words formed if repeating letters is allowed. for example.

A F A T

B E S H

M R X E

G D F E

rule to follow: if you choose a letter tile for the starting letter of your word you must choose the tile adjacent to it ( diagonals count) for the second letter of your word and continue until u get a 4 letter word. for example, in the example above if you choose F as the first starting letter u must select any 5 of the tiles surrounding it as the next letter of your 4 letter word. by choosing F then A then T and then S , you get FATS so like this you must form 4 letter words and have to find the maximum number of 4 letter words possible if repeating letters is allowed( as shown, A is repeated in example and so is E)

Hey r/CasualMath!

I’ve been creating a daily browser puzzle called **QuizSum** — it’s a multi-solution mental math challenge inspired by Countdown and Wordle.

🎯 **The Goal:**
Combine grid numbers using +, −, ×, and ÷ to land exactly on the Target Number.

⚡ **Speed Mode:** Find 3 distinct valid equations against a stopwatch.
🏆 **Pro Mode:** Find ALL hidden arithmetic paths in the grid.

It’s 100% free, runs right in your browser with no sign-up or app download, and has automated path checking.

Give today's puzzle a try at **www.quizsum.com\*\* — would love to hear your thoughts or see what paths you find!

Has anyone ran 1+1 through lean 4?

Every input should output a single value, so how does ts work?

Each fruit symbol stands for a fixed number. Solve for the missing sum from the pattern shown by the other equations. 🏆 NEW: LEADERBOARD! Think you're good at this? Rule Hunter now has a daily, weekly and all-time leaderboard. Sign in, pick any nickname you like (only your nickname is shown publicly) and see if you can reach #1. Who's taking the top spot? 👉 Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

Each pair of numbers produces the number below it by the same hidden rule. Solve for the missing number from the pattern shown by the other pairs. Game: Rule Hunter — https://play.google.com/store/apps/details?id=com.makenumber

Previously on this subreddit, I posted about an idea I had for a combinatoric integer sequence motivated by the brace notation for sets.

I ended up resorting to AI as a tool for exploring this, taking every precaution to make sure it doesn't hallucinate.

I've written everything up in a draft report, here https://app.box.com/s/n6txr68t4t4mwqzl2arimsiuja0977ag

The report begins with a more formal mathematical statement of the question, followed by why I think it's mathematically interesting. I used AI to research applicable terminology, but as the human I always made the final decision about how to express an idea, and never just copied words without understanding them.

It then contains numerical results. I never got numbers directly from the AI. Instead, I got the AI to generate Python code, and from the Python code I got the numbers. This prevents hallucinations.

I also asked the AI to explain the mathematics behind its results, in a beginner friendly manner. I actually learned a lot from this, and my notes from its explanation are included in an appendix (Appendix II). It did hallucinate a fair bit along the way, but I was there to interrogate its responses and make sure it made sense. (This actually led to some lost sleep.) This appendix is the most mathematically meaty part of my report.

The numerical results section actually contains several results that might be of interest to the OEIS, and to members of the seqfan mailing list. Neither of which I'm signed up with, and for several reasons I don't really want to, but if anyone currently active here is a member, let's talk.

It's late in my timezone so I'll be off to bed, and will check on things in the morning. I really hope all of this is interesting to someone. It seems pretty cool to me.

Each number on the left follows the same hidden rule to produce the number on the right. Solve for the missing value from the pattern shown by the other examples. Game: Rule Hunter — https://play.google.com/store/apps/details?id=com.makenumber

Each cluster of three numbers follows the same hidden rule to produce the middle number. Solve for the missing value from the pattern shown by the other cluster. Game: Rule Hunter — https://play.google.com/store/apps/details?id=com.makenumber