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1,698,447 questions
23 votes
3 answers
6k views
The cow in the field problem (intersecting circular areas)
What length of rope should be used to tie a cow to an exterior fence post of a circular field so that the cow can only graze half of the grass within that field? updated: To be clear: the cow should ...
43 votes
23 answers
4k views
Can you recommend a decent online or software calculator?
I'm looking for an online or software calculator that can show me the history of items I typed in, much like an expensive Ti calculator. Can you recommend any?
20 votes
4 answers
2k views
Why is the matrix-defined Cross Product of two 3D vectors always orthogonal?
By matrix-defined, I mean $$\left<a,b,c\right>\times\left<d,e,f\right> = \left| \begin{array}{ccc} i & j & k\\ a & b & c\\ d & e & f \end{array} \right|$...
18 votes
10 answers
8k views
What is a real number (also rational, decimal, integer, natural, cardinal, ordinal...)?
In mathematics, there seem to be a lot of different types of numbers. What exactly are: Real numbers Integers Rational numbers Decimals Complex numbers Natural numbers Cardinals Ordinals And as ...
14 votes
2 answers
4k views
How do you calculate the semi-minor axis of an ellipsoid?
Given the semi-major axis and a flattening factor, is it possible to calculate the semi-minor axis?
371 votes
31 answers
66k views
Is it true that $0.999999999\ldots=1$?
I'm told by smart people that $$0.999999999\ldots=1$$ and I believe them, but is there a proof that explains why this is?
48 votes
8 answers
4k views
How are we able to calculate specific numbers in the Fibonacci Sequence?
I was reading up on the Fibonacci Sequence, $1,1,2,3,5,8,13,\ldots $ when I noticed some were able to calculate specific numbers. So far I've only figured out creating an array and counting to the ...
54 votes
9 answers
10k views
What is your favorite online graphing tool?
I'm looking for a nice, quick online graphing tool. The ability to link to, or embed the output would be handy, too.
76 votes
20 answers
48k views
How can you prove that the square root of two is irrational?
I have read a few proofs that $\sqrt{2}$ is irrational. I have never, however, been able to really grasp what they were talking about. Is there a simplified proof that $\sqrt{2}$ is irrational?
143 votes
22 answers
83k views
List of interesting math podcasts? [closed]
mathfactor is one I listen to. Does anyone else have a recommendation?
202 votes
9 answers
15k views
What Does it Really Mean to Have Different Kinds of Infinities?
Can someone explain to me how there can be different kinds of infinities? I was reading "The man who loved only numbers" by Paul Hoffman and came across the concept of countable and uncountable ...
53 votes
2 answers
2k views
Would Relational Calculus be Turing-Complete if it Allowed Unsafe Queries?
My understanding about Codd's concept of "safe queries" was created to ensure that a query would always terminate. One key ability of a Turing machine is that it can work on infinite calculations (...