For questions about the motivation behind mathematical concepts and results. These are often "why" questions.
Questions tagged [motivation]
419 questions
5
votes
1 answer
What motivates the arithmetic-geometric mean?
What motivates the arithmetic-geometric mean? What inspires it? I understand how to calculate this mean but do not understand what might prompt a mathematician to pursue such a mean in the first place.
Is there a notion or mental image that conjures…
thb
- 449
3
votes
1 answer
Motivation behind this proof of the Basel problem?
On a past paper from our examination committee there seems to be a proof to the Basel problem that is plucked out of thin air. It doesn't match any of the proofs on Wikipedia (at least by first glance) and I can't find it anywhere on Google through…
Pen and Paper
- 1,371
1
vote
1 answer
How to focus for long hours?
I'm currently working on my A levels and would like to know about how to focus for longer hours and stay motivated? I'm also working on STEP Support program for entry into Cambridge and would like to know if there are certain tricks to be able to do…
Grisha Ukugo
- 23
1
vote
1 answer
Motivate why $a^{-n}$ equals to $\frac{1}{a^n}$
I have to prove that $a^{-n} = \frac{1}{a^n}$ with $\frac{3^4}{3^7}$, but before I can do that I have to understand the background.
The background says:
we know that $\frac{3^4}{3^7} = \frac{1}{3^3}$ and that $3^{4-7} = 3^{-3} = \frac{1}{3^3}$
I…
0
votes
0 answers
definition and derivation of sine - unit circle - rectangle
sine is defined as:
$sin(\alpha) = \frac{opposite}{hypotenuse}$
My questions are:
why is sine only defined on right angles?
where does the definition comes from/is derived?
is the unit circle used to define sine or just to show the values?
as far…
JaySmi
- 1