Difference between revisions of "User talk:Bobthesmartypants/Sandbox"
(→Fermat point) |
(→Fermat point) |
||
Line 460: | Line 460: | ||
draw((0,3)--4*dir(60),red+linetype("8 8 0 8")); | draw((0,3)--4*dir(60),red+linetype("8 8 0 8")); | ||
draw((4,0)--3*dir(30),red+linetype("8 8 0 8"));</asy> | draw((4,0)--3*dir(30),red+linetype("8 8 0 8"));</asy> | ||
+ | |||
+ | ==cenn driagrma== |
Revision as of 00:55, 8 June 2014
Contents
Bobthesmartypants's Sandbox
Solution 1
First, continue to hit
at
. Also continue
to hit
at
.
We have that . Because
, we have
.
Similarly, because , we have
.
Therefore, .
We also have that because
is a parallelogram, and
.
Therefore, . This means that
, so
.
Therefore, .
Solution 2
Note that is rational and
is not divisible by
nor
because
.
This means the decimal representation of is a repeating decimal.
Let us set as the block that repeats in the repeating decimal:
.
( written without the overline used to signify one number so won't confuse with notation for repeating decimal)
The fractional representation of this repeating decimal would be .
Taking the reciprocal of both sides you get .
Multiplying both sides by gives
.
Since we divide
on both sides of the equation to get
.
Because is not divisible by
(therefore
) since
and
is prime, it follows that
.
Picture 1
Picture 2
physics problem
Solution
inscribed triangle
moar images
yay
solution reflection
origami
combos
circles
more circles
checkerboasrd
Fermat point