How many dimensions does a circle have?
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How many dimensions does a circle have?

Is a circle just a line (therefore 1 dimension) or is it a 2-dimensional object because it occupies some surface? Thanks in advance!

Published: Aug 21, 2026

Use part 1 of the Fundamental Theorem of Calculus to find the derivative of the following function.
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Use part 1 of the Fundamental Theorem of Calculus to find the derivative of the following function.

$$y = \int_\sqrt x^{\pi/4} \theta \tan\theta \, d\theta$$ I'm using the property of definite integrals that says $\int_b^a f(x) \, dx = -\int_a^b f(x...

Published: Aug 21, 2026

Can rational numbers have decimals?
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Can rational numbers have decimals?

I had a question in my exam paper - Which of the following is not a rational number? a) $\sqrt{25}$ b) $\sqrt{45}$ c) $\sqrt\frac{256}{225}$ d) $\frac{3}{...

Published: Aug 21, 2026

What's the value of $x$ in the following equation?
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What's the value of $x$ in the following equation?

So this is how I approached this question, the above equations could be simplified to : $$a = \frac{4(b+c)}{b+c+4}\tag{1!}$$ $$b = \frac{10(a+c)}{a+c+10}\...

Published: Aug 21, 2026

Why is $i^3$ (the complex number
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Why is $i^3$ (the complex number "$i$") equal to $-i$ instead of $i$? [duplicate]

$$i^3=iii=\sqrt{-1}\sqrt{-1}\sqrt{-1}=\sqrt{(-1)(-1)(-1)}=\sqrt{-1}=i $$ Please take a look at the equation above. What am I doing wrong to understand $i^...

Published: Aug 21, 2026

Probability of a dice game: win, lose or draw.
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Probability of a dice game: win, lose or draw.

$C$ and $J$ play a game. $C$ always starts. $C$ rolls a fair dice first and wins if he throws an even number. If not, then $J$ rolls the dice. If she roll...

Published: Aug 21, 2026

Topology without tears
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Topology without tears

I have started reading the book Topology Without Tears by Sidney A. Morris. I have read the first chapter and so far it reads well. However, the name of t...

Published: Aug 21, 2026

What is the usage of Bernoulli triangle?
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What is the usage of Bernoulli triangle?

I know that Pascal triangle is very usfeul in many fields of mathematics. I typed in google Bernoulli triangle and couldn't find any usage of it, eve...

Published: Aug 21, 2026

How to find a transformation matrix, given coordinates of two triangles in $R^2$
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How to find a transformation matrix, given coordinates of two triangles in $R^2$

I am an undergraduate student, and today I was given two triangles, $T_1$ (green) and $T_2$ (blue) in $R^2$: I was then asked to find the transformation m...

Published: Aug 21, 2026

Function for a hexagonal 2-dimensional grid
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Function for a hexagonal 2-dimensional grid

I can make a "square" $2$D sine wave pattern with the function $f(x,y) = \cos(x) + \cos(y)$: What is the function to make a hexagonal pattern of the same ...

Published: Aug 21, 2026

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