I have seen this method used in discrete maths where we treat the following equation:

an = an-1 + an-2

as:

x^2^ = x + 1

then solve the equation and let's say we got roots r1 and r2 then the recurrence relationship can be written as:

an=c1*(r1)^n^ + c2*(r2)^n^

what do we do to expand that recurrence relation so that this patten emerge?

Hi! I was trying to mathematically solve a positioning problem for a game I am playing and while I was able to postulate the problem; I feel my education has fallen me short to find a solution. The problem is as follows:

• You have N shapes compromized of any number of vertices declared as integer offsets from their origin point (the origin point counts as a vertex).

• Out of the N shapes you have to pick a group of Y size that maximizes the number of overlapping vertices between them with the following rules:

  -- The origin point of each shape must be placed on a 2D integer grid.

  -- The origin point of each shape must be different from each other shapes origin point.

  -- The shapes can be rotated in steps of 90º any number of times.

  -- For a vertex to count as overlapping it must be the exact same position as the vertex of at least one other shape and one of the vertices must be the origin point of a shape.

Where could I read material to advance in this problem? Is there an algorithm for these problems?

I'm just going to keep sharing these. I have yet to read an article on this substack that I wouldn't recommend.

If anyone is bored and wants a fun project for lemmy - find the minimim ratio of Posts to Comments over time that objectively determine an unmarked account to be a bot.

I've been loving every post from Senia.

As a recent reddit ex-pat, I've been missing the discussions of these, so I'm posting the latest post here to spread the love.

There is a certain class of mathematical problem whose importance grows rather than diminishes with the passage of time. The Riemann Hypothesis belongs firmly in this class. Proposed in a single eight-page memoir by Bernhard Riemann in 1859 — a paper titled Über die Anzahl der Primzahlen unter einer gegebenen Größe ("On the number of primes less than a given quantity") — it has resisted the sustained assault of brilliant mathematical minds across four generations. It stands today as one of the seven Millennium Prize Problems, carrying a one-million-dollar reward from the Clay Mathematics Institute, and it is the only one of those seven with the added distinction of appearing on Hilbert's famous 1900 list of problems for the twentieth century.

...

withdrawal statement for paper 1

withdrawal paper 2

withdrawal paper 3

overview of all results is here:

https://github.com/openai/math/blob/main/overview.pdf

Several are fields medal worthy results. One proves the Riemann hypothesis for Re(z) >7/8, which is a substantial improvement over previous results

I'm terrible at math, but I had this thought while playing around in Blender. The car near the pole needs to turn the wheel to maintain distance, but the car on the equator drives in a "straight" line. At what distance from the pole is the transition? I hope this makes the question clear, I ran into a character limit in the title.

Cross posted from https://lemmy.world/post/51865355

This declaration was written Sept 10, and already has over 5,000 signatures

Over the last few months, the mathematical capabilities of LLMs have improved dramatically, to the point that they can solve major outstanding problems in many fields of mathematics. However, the push by AI companies to solve mathematical problems as a benchmark is detrimental to the science of mathematics, and to the mathematical community. The goals of the AI companies and the goals of the mathematical community are severely misaligned. We see these as part of broader alignment issues impacting other scientific and creative professions, as well as the whole of society. more

Just something that came out on my feed and looks like a good new resource

Is there a way to make the function

f(w,t)=sin(wt)/w

defined at w = 0?

I want to achieve better numerical stability, and make it continuous everywhere.

Observation: Using limw->0 f(w,t)

I know that at w = 0:

f(0,t) = t

Is it possible to improve this function? I would be really glad to know and why, how. Thank you in advance!

I really do not want to code in smth like: if w < 0.001 { x = t; }

Background notes: My equation also has constant v coefficient, but I removed it for simplicity. f(w,t)=v*sin(wt)/w

If I derived this correctly this should be x component of a motion of a car that rotates with rate w. It goes with const speed and const steer.

These are consts: v - speed, l - base length(dist from rear to front shaft), a - steering angle.

w(a) is defined idk if correctly. w(a) = (vsin(2a))/(2*l) I just logically added proportions, projections, imagining a rear wheel powered car. Put some values I am somewhat confident in, such as: w(0) = 0 w(π/2) = 0