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Questions tagged [recreational-mathematics]

Mathematics done just for fun, often disjoint from typical school mathematics curriculum. Also see the [puzzle] and [contest-math] tags.

Recreational mathematics is a general term for mathematical problems studied for the sake of pure intellectual curiosity, or just for the enjoyment of thinking about mathematics, without necessarily having any practical application or expectation of deep theoretical results.

Recreational mathematics problems are often easy to understand even for people without an extensive mathematical education, even if the theory they lead to may turn out to be surprisingly deep. Thus, recreational mathematics can serve to attract the curiosity of non-mathematicians and to inspire them to develop their mathematical skills further.

Many typical recreational mathematics problems fall into the fields of discrete mathematics (combinatorics, elementary number theory, etc.), probability theory and geometry. Important contributors to recreational mathematics are Sam Loyd and Martin Gardner.

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Patterns of 1-gon numbers

The general pattern of the n-gonal numbers is that the mth n-gonal number is equal to $$\left(\frac{n}{2}-1\right)m^2-\left(\frac{n}{2}-2\right)m .$$ For instance, the formula of the triangular numbers is $$\frac{m(m+1)}{2}$$ which can be expanded…
Mark Smith
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Need help finding a conversion between units

I am measuring an angle with a gyroscope, but it gives outputs 0-100. I wish to convert this into degrees; Actual (degrees) Gyro Reading 0 100 90 0 I have also measured (although I am not sure the reliablity of these data…
tophatcollection
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Why doesn't math introduce an axiom $0÷0=0$ as a means to claim the multiplication by $0$ is irreversible?

Andy my friend claims that $0=X\cdot 0$ where $X$ is an arbitrary value, $0\div 0=X$, and thus $0/0$ can be assigned to an arbitrary value. But he mistakenly considers $0÷0=1$ or the multiplication by $0$ is always reversible. As far as I know,…
User
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Elegant pattern in the standard London Dartboard$?$

The image below is of a standard dartboard I was just wondering why this sequence of numbers was used in the first place. Is there any special and beautiful sequence hidden in this dartboard$?$ I tried finding some by experimenting with the…
MathStackexchangeIsNotSoBad
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He would like to get and array where all entries are divisible by 2013.Then how many arrays are possible..?

Ramesh is given a $2013\times2013$ array of integers between $1$ and $2013$ both inclusive. He is allowed only $2$ operation. 1)Choose a row,subtract $1$ from each entry. 2)Choose a column ,add $1$ to each entry. He would like to get and array where…
maths lover
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Arithmetic progressions of perfect powers

Find the largest positive integer $n<100$, such that there exists an arithmetic progression of positive integers $a_1,a_2,...,a_n$ with the following properties. $1)$ All numbers $a_2,a_3,...,a_{n−1}$ are powers of positive integers, that is…
KLG
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Probability that a uniformly selected point in the interior of sphere...

Probability that a uniformly selected point in the interior of sphere of a given arbitrary radius (for the purposes of this, we will say 2022) is closer to the surface of the sphere than the center. I was imagining taking a slice of the sphere and…
Kevin Perez
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Nicole Oserme and mathematics of Middle Ages

Does anybody know of any textbooks that discuss some of the work by Nicole Oserme and in the period of the Middle Ages ?
Veak
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How do I calculate how much time the video will last with a different player velocity?

First, this is my first post in math.se, if this question is not adequate to this site, please show me where it would be fit ok ? And sorry in avance. Yesterday I was seeing a video in YouTube in enhanced speed and tried to calculate how long the…
Nelson Teixeira
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Building a circle containing a specific number of points on a plane

Given a 2-dimensional plane containing $n$ random points, prove that it's always possible to build a circle containing exactly $k$ points; where $n\gg k$. A friend told me this problem and the solution a few months ago, but I completely forgot it. I…
JonathanReez
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"Mathematical Circles (Russian Experience)", Chapter Zero, P11

I request a hint, clarification (if needed), or your approval (if my doutful solution is correct) for this problem: Problem 11. A teacher drew several circles on a sheet of paper. Then he asked a student "How many circles are there?" "Seven," was…
Sophi
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"Mathematical Circles (Russian Experience)", Chapter Zero, P9

I request a hint, clarification (if needed), or your approval (if my doutful solution is correct) for this problem: Problem 9. Peter said: "The day before yesterday I was 10, but I will turn 13 in the next year." Is this possible? Every hint or…
Sophi
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Diagonal Sine Wave

I found the equation $$ \frac{(y-x)\sqrt{2}}{2}=\sin\left(\frac{(y+x)\sqrt{2}}{2}\right) $$ for a sine wave rotated $45^\circ$. Based on the shape, I know the relation is a one to one function. It stands to reason, then, that you could isolate y and…
Nate
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Given $\theta_1,\theta_2,\theta_3$, does there exist solution for $e^{i\theta_1 T} + e^{i\theta_2 T} + e^{i\theta_3 T} =0$?

I came up with the following problem. Given mutually different $\theta_1,\ldots,\theta_3\in\mathbb R-\{0\}$, does there exist $T\in \mathbb R$ such that $$e^{i\theta_1 T} + e^{i\theta_2 T} + e^{i\theta_3 T}=0?$$ For simpler problem of determining…
Laplacian
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Why was it valid to invent the imaginary unit, $i$?

I understand that imaginary numbers have turned out to be very useful but aren't there rules in mathematics that prevent you from inventing objects which, as far as I can see, contradict some mathematical rules? To me, defining a number to be the…
Garincha
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