Timeline for How to raise a number to a power geometrically.
Current License: CC BY-SA 3.0
22 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2016 at 17:33 | comment | added | Blue | For integer powers (positive, negative, or zero), see this answer. | |
| Aug 28, 2016 at 17:13 | comment | added | Abdur Rahman | @RickyDemer I did know that for the under-root of 2. But, it is impossible to raise a line-segment to certain powers, if I am right. | |
| Aug 28, 2016 at 17:10 | comment | added | user57159 | No, since the Pythagorean Theorem gives an easy method of constructing some irrational ratios. | |
| Aug 28, 2016 at 17:09 | comment | added | Abdur Rahman | @RickyDemer Ahhh! Basically it is is not possible to geometrically construct a^x where the outcome is irrational. So, we cannot construct 2^(1/3) since it is irrational. Have I understood right? | |
| Aug 28, 2016 at 17:03 | history | edited | Abdur Rahman | CC BY-SA 3.0 |
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| Aug 28, 2016 at 16:57 | comment | added | Abdur Rahman | @Christian Well, thank you for admitting that. I do not know much about n-dimensions and all that. | |
| Aug 28, 2016 at 16:57 | comment | added | user57159 | He's talking about the theorem on the page my initial comment linked to. | |
| Aug 28, 2016 at 16:55 | comment | added | Abdur Rahman | @Aretino I did not know that. I should edit my question. Also, can you please provide the theorem you are talking about? I know only college level mathematics. : ) | |
| Aug 28, 2016 at 16:54 | comment | added | Abdur Rahman | @RickyDemer I am sorry your comment is entirely incomprehensible. The second part though; you see I am talking about just Euclidean geometry. We are taught how to exponentiate algebraically, but, I want to find a meaning without algebra. Sorry, if I have offended you. | |
| Aug 28, 2016 at 16:48 | comment | added | Intelligenti pauca | Already raising a segment to power $1/3$ is impossible using straightedge and compass. Which instruments would be allowed? | |
| Aug 28, 2016 at 16:48 | comment | added | user57159 | I can't "do it ... than a unit". That doesn't stop a^1 from being meaningful even when 1 isn't. | |
| Aug 28, 2016 at 16:44 | comment | added | Abdur Rahman | @RickyDemer You did choose '1' as a unit. I am talking about Euclidean geometry. I give you line-segment A and tell you to raise it to the power a line-segment B; not algebraically. How can you do it without knowing whether line-segment B is less than or greater than a unit? | |
| Aug 28, 2016 at 16:41 | history | edited | Abdur Rahman | CC BY-SA 3.0 |
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| Aug 28, 2016 at 16:41 | answer | added | user345851 | timeline score: 3 | |
| Aug 28, 2016 at 16:39 | comment | added | Christian | @AbdurRahman My apologies; I had misinterpreted the question. After seeing what you meant my comment is hardly applicable | |
| Aug 28, 2016 at 16:39 | comment | added | user57159 | @AbdurRahman : a^1 = a regardless of what unit is chosen. | |
| Aug 28, 2016 at 16:36 | comment | added | Abdur Rahman | @ShubhamKumar Yes, I do realize a unit will be necessary as a^1 will otherwise be meaningless. | |
| Aug 28, 2016 at 16:35 | comment | added | user57159 | en.wikipedia.org/wiki/Doubling_the_cube | |
| Aug 28, 2016 at 16:33 | comment | added | user345851 | do you mean to construct a number $a^n$ from a given segment of length $a$ and $1$? | |
| Aug 28, 2016 at 16:32 | comment | added | Abdur Rahman | @Christian What about fractional exponents? And, how exactly can I illustrate the concept on n-dimensional cube in Euclidean geometry? | |
| Aug 28, 2016 at 16:29 | comment | added | Christian | For integer exponents, you could consider $a^n$ as the volume of an $n$-dimensional cube with side lengths of $a$ | |
| Aug 28, 2016 at 16:23 | history | asked | Abdur Rahman | CC BY-SA 3.0 |