Difference between revisions of "User talk:Bobthesmartypants/Sandbox"
(→cenn driagrma) |
(→cyclic square) |
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<asy> | <asy> | ||
− | + | draw(Circle((0,0),0.5)); | |
− | + | draw(0.5*dir(15)--0.5*dir(105)--0.5*dir(195)--0.5*dir(285)--cycle); | |
− | label(" | + | label(scale(6)*"CS",(0,0)); |
</asy> | </asy> | ||
Revision as of 21:12, 26 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
cenn driagrma
cyclic square