Difference between revisions of "User talk:Bobthesmartypants/Sandbox"
(→yay) |
(→solution reflection) |
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Line 351: | Line 351: | ||
label("$C$",dir(0),dir(0)); | label("$C$",dir(0),dir(0)); | ||
label("$C'$",dir(30),dir(30));</asy> | label("$C'$",dir(30),dir(30));</asy> | ||
+ | |||
+ | |||
+ | <asy> | ||
+ | for(int i = 0; i < 60; ++i){ | ||
+ | draw((0,0)--dir(6*i)); | ||
+ | draw(dir(6*i)--dir(6*i+6),linetype("8 8")); | ||
+ | } | ||
+ | draw(1.2*dir(3)--1.2*dir(177)); | ||
+ | label("Diagram not to Scale",dir(-90),dir(-90));</asy> |
Revision as of 18:13, 11 May 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