Does someone know how to prove this:
An angle of x such that 0 < x < 90 degrees can be constructed with a ruler if and only if tan(x) is a rational number.
Thanks in advance.
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Does someone know how to prove this:
An angle of x such that 0 < x < 90 degrees can be constructed with a ruler if and only if tan(x) is a rational number.
Thanks in advance.
Hello, BrainMan!
The proof is simple in one direction . . .
Quote:
An angle θ such that 0° < θ < 90°
can be constructed with a ruler if and only if tan θ is a rational number.
Ifis a rational number
, where
are positive integers,
. . we can construct angle
Code:* R
* |
* |
* | a
* |
* θ |
- - * - - - - - - - - * - -
P b Q
On a horizontal line, mark points P and Q so that: PQ = b
At Q, erect a perpendicular QR so that: QR = a
Draw line segment PR.
. . Then: ./ RPQ = θ
And how do we erect (construct) a perpendicular with only a ruler?Quote:
Originally Posted by Soroban
Yes, how can you construct a and b (or (a,0) and (0, b)) without a compass?
BrainMan, *cough-cough*, taking math-348 this summer @ mcgill U? (Wait)
found it strange that last time u posted about assignment #2Q5.
:P
hey, you're looking for help too, right?
lol, yeah XD, (Rofl), u can't find this Question anywhere T^T. I see that we are very similar to each other lol. We both seek answers online INSTEAD OF working our asses off :P.
I was searching for assignment2Q5, and i landed on ur post and i found it SOO strange that ur Q was the same as my assignment and u posted it like the day it was released or something lol. Anyways, i was suspicions and now here I am searching for the same Question as u have right now :p and landed on ur post (Lipssealed).
Can't seem to find Q1 (proof >_<, they discuss about it, but no proofs), and Q3 (don't understand), i found all other Qs or did them manually. (Giggle)♥ internet ♥