# Questions tagged [big-list]

Questions asking for a "big list" of examples, illustrations, etc. Ask only when the topic is compelling, and please do not use this as the only tag for a question.

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### Measure of error in smoothness of approximation of sphere

I'm meshing a sphere and am solving a physics problem on this. What I want to show is that the error in the model scales like$$\varepsilon = \epsilon^p,$$ where $\epsilon$ is the "error" in the ...
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### Real life applications of the Lefschetz fixed point theorem

I'm looking for real life applications of the Lefschetz fixed point theorem. I encountered this link: https://mathoverflow.net/questions/127045/fixed-point-theorems However, I was hoping for ...
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### Big list: collecting results of diagram chasing

I plan giving a homework problem on linear algebra for my students and my idea was to collect many results of diagram chasing. Could you help me and give me some results of diagram chasing you know? ...
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### Rational approximations for $\pi$ using Fibonacci numbers?

It is (well?) known that $$\frac{\pi} 4 = \sum_{k=1}^\infty \arctan \left ( \frac1{F_{2k+1}} \right )$$ Where $F_k$ denotes the $k$-th Fibonacci number. However, any truncation of this sum is ...
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### Recommendations for differential geometry textbooks that develop geometric intuition.

I'm currently self-studying complex analysis (CA), and reading "Visual Complex Analysis" by Tristan Needham. I'm absolutely fascinated by how much geometric intuition he provides for the key findings ...
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### Mathematical Consequences of $P=NP$ or $P\neq NP$ [closed]

It is common in mathematics to assume some unknown hypothesis or conjecture to be true or false, and then prove results dependent on said assumption. This can lead to many interesting developments ...
I have been studying linear algebra for some time now, and I have seen some really interesting applications of linear transformation and matrices such as finding the integral $\int x^2e^x dx$. Does ...