Hello, mfetch22!
Can anybody explain to me some of the methods used
to approxiamtely construct a line segement of length ?
We can always construct a angle.
Construct an equilateral triangle and bisect one of its angles.
Code:
A
* o *
* | o *
* | o *
* |1 o
| o
* | * o
* *O * o
* /| * o
1 / | o
* /30| * o
* / |1 * o
*/ | * o
P - - - + - * * * - - + - - - - - - + - - - - - - o - - Q
C B D E F
: - - 1 - - : - - 1 - - : - - 1 - - :
We have a circle with center and radius 1.
is a diameter.
Line is tangent to circle at
Construct segment so that
From , mark off three radii on
. .
Draw segment
We have: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Proof
In right triangle
Then: .
In right triangle
. .
Therefore: .
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
From: .Mathematical Puzzles and Pastimes, Aaron Bakst
. . . . . . . . D. Van Nostrand Company, Inc., 1954