Linked Questions
44 questions linked to/from Visually stunning math concepts which are easy to explain
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Visualising the sum of the first $n$ positive odd integers [duplicate]
Using the fact that $1+2+\cdots+n=\frac{n(n+1)}{2}$, we can deduce that sum of first $n$ positive odd integers is $n^2$. However, is there a way of finding the sum of $1+3+5+\cdots+(2n-1)$ visually?
- 174
140
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24
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Visually deceptive "proofs" which are mathematically wrong
Related: Visually stunning math concepts which are easy to explain
Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually ...
92
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34
answers
25k
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Easy math proofs or visual examples to make high school students enthusiastic about math [closed]
I'm a teacher in mathematics at a high school. Math has fascinated me for almost my entire life, so I would like to bring that enthusiasm to my students with beautiful yet easy to understand proofs or ...
- 2,132
89
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4
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Why is the Möbius strip not orientable?
I am trying to understand the notion of an orientable manifold.
Let M be a smooth n-manifold. We say that M is orientable if and only if there exists an atlas $A = \{(U_{\alpha}, \phi_{\alpha})\}$ ...
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53
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4
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What is the explanation for this visual proof of the sum of squares?
Supposedly the following proves the sum of the first-$n$-squares formula given the sum of the first $n$ numbers formula, but I don't understand it.
- 2,958
7
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22
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Proving $x^2+x+1\gt0$
I was doing a question recently, and it came down to proving that $x^2+x+1\gt0$. There are of course many different methods for proving it, and I want to ask the people here for as many ways as you ...
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19
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7
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Pythagorean Theorem Proof Without Words 6
Your punishment for awarding me a "Nice Question" badge for my last question is that I'm going to post another one from Proofs without Words.
How does the attached figure prove the Pythagorean ...
- 3,425
40
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3
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Textbooks for visual learners
Perhaps this question has already been asked (if so, please let me know) but I am looking for books that appeal to visual learners.
I discovered that I am able to understand concepts much quicker ...
- 4,285
12
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5
answers
1k
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If sum of triangle angles is $180$ degrees, how $\sin(270)$ is possible?
I'm not new to trigonometry, but this question always bothers me.
As it is in Wolfram MathWorld-
$$
\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}
$$
We know that the sum of the angles in a ...
3
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8
answers
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Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?
Why $\cos(-\theta)$ gives positive values while in case of sine it is negative?
I mean
$\cos(-\theta) = +\cos(\theta)$
$\sin(-\theta) = -\sin(\theta)$
$\tan(-\theta) = -\tan(\theta)$
and please ...
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21
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4
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1k
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What areas of math can be tackled by artificial intelligence?
Artificial intelligence is nearing, with image/speech recognition, chess/go engines etc. My question is, what areas of math that are interesting to mathematicians, is likely to be the first to be able ...
- 390
6
votes
5
answers
6k
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Why do some series converge and others diverge?
Why do some series converge and others diverge; what is the intuition behind this? For example, why does the harmonic series diverge, but the series concerning the Basel Problem converges?
To ...
- 1,159
2
votes
5
answers
1k
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Speechless mathematical proofs.
Do you have proofs without word?
Your proofs are not necessary has zero word, you may add a bit explanations.
As an example, I has a "Speechless proof" for
$$\frac{1}{4}+\frac{1}{4^2}+\frac{1}{4^3}+....
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7
votes
3
answers
6k
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Riddle: A special $6$-digit number
Here is a riddle:
Riddle: I am thinking about a $6$-digit number
$
\underline{ }\,
\underline{ }\,
\underline{ }\,
\underline{ }\,
\underline{ }\,
\underline{ }
$
(no leading zeros). All digits ...
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53
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1
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Pattern "inside" prime numbers
Update $(2020)$
I've observed a possible characterization and a possible parametrization of the pattern, and I've additionally rewritten the entire post with more details and better definitions.
It ...
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