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1500 questions
80
votes
22 answers
An example of a problem which is difficult but is made easier when a diagram is drawn
I am writing a blog post related to problem solving and one of the main techniques used in problem solving is drawing a diagram. Essentially, I want to illustrate that some hard problems (for example, word problems) can be done fairly easily when…
Jeel Shah
- 9,586
80
votes
10 answers
Is there a shape with infinite area but finite perimeter?
Is this really possible? Is there any other example of this other than the Koch Snowflake? If so can you prove that example to be true?
Chris Truong
- 801
79
votes
2 answers
What are the formal names of operands and results for basic operations?
I'm trying to mentally summarize the names of the operands for basic operations. I've got this so far: Addition: Augend + Addend = Sum. Subtraction: Minuend - Subtrahend = Difference. Multiplication: Multiplicand × Multiplier = Product. Generally,…
trw
- 1,083
79
votes
4 answers
Limit $\frac{x^2y}{x^4+y^2}$ is found using polar coordinates but it is not supposed to exist.
Consider the following 2-variable function: $$f(x,y) = \frac{x^2y}{x^4+y^2}$$ I would like to find the limit of this function as $(x,y) \rightarrow (0,0)$. I used polar coordinates instead of solving explicitly in $\mathbb R^2 $, and it went as the…
b0neval
- 1,500
79
votes
5 answers
What is the geometry in algebraic geometry?
Coming from a physics background, my understanding of geometry (in a very generic sense) is that it involves taking a space and adding some extra structure to it. The extra structure takes some local data about the space as its input and outputs…
d_b
- 1,085
79
votes
4 answers
What is the difference between a Ring and an Algebra?
In mathematics, I want to know what is indeed the difference between a ring and an algebra ?
user70795
- 931
79
votes
9 answers
What is the math behind the game Spot It?
I just purchased the game Spot It . As per this site , the structure of the game is as follows: Game has 55 round playing cards. Each card has eight randomly placed symbols. There are a total of 50 different symbols through the deck. The most…
Javid Jamae
- 894
79
votes
13 answers
Why are addition and multiplication commutative, but not exponentiation?
We know that the addition and multiplication operators are both commutative, and the exponentiation operator is not. My question is why . As background there are plenty of mathematical schemes that can be used to define these operators. One of these…
rob levin
- 791
79
votes
9 answers
What do $\pi$ and $e$ stand for in the normal distribution formula?
I'm a beginner in mathematics and there is one thing that I've been wondering about recently. The formula for the normal distribution is: $$f(x)=\frac{1}{\sqrt{2\pi\sigma^2}}e^{-\displaystyle{\frac{(x-\mu)^2}{2\sigma^2}}},$$ However, what are $e$…
pimvdb
- 1,293
79
votes
9 answers
Probability of 3 people in a room of 30 having the same birthday
I have been looking at the birthday problem (http://en.wikipedia.org/wiki/Birthday_problem) and I am trying to figure out what the probability of 3 people sharing a birthday in a room of 30 people is. (Instead of 2). I thought I understood the…
irl_irl
- 893
79
votes
5 answers
Why should I care about adjoint functors
I am comfortable with the definition of adjoint functors. I have done a few exercises proving that certain pairs of functors are adjoint (tensor and hom, sheafification and forgetful, direct image and inverse image of sheaves, spec and global…
DBr
- 5,070
79
votes
6 answers
How to generate random points on a sphere?
How do I generate $1000$ points $\left(x, y, z\right)$ and make sure they land on a sphere whose center is $\left(0, 0, 0\right)$ and its diameter is $20$ ?. Simply, how do I manipulate a point's coordinates so that the point lies on the sphere's…
Filip
- 799
79
votes
13 answers
Why there is no sign of logic symbols in mathematical texts?
Either in undergraduate or graduate textbooks on Mathematics (Real/Complex Analysis, General Topology, Differential Geometry, ...), I never saw symbols $\Rightarrow$, $\iff$, $\forall$, $\exists$, etc. Instead, I just see their "read as" or…
MKR
- 1,078
- 2
- 9
- 19
78
votes
2 answers
Determinant of a rank $1$ update of a scalar matrix, or characteristic polynomial of a rank $1$ matrix
This question aims to create an " abstract duplicate " of numerous questions that ask about determinants of specific matrices (I may have missed a few): Characteristic polynomial of a matrix of $1$'s Eigenvalues of the rank one matrix $uv^T$…
Marc van Leeuwen
- 120,872
78
votes
5 answers
Help me solve my father's riddle and get my book back
My father is a mathteacher and as such he regards asking tricky questions and playing mathematical pranks on me once in a while as part of his parental duty. So today before leaving home he sneaked into my room and took the book I am currently…
user161516