Posted by deana on Wednesday, January 25, 2012 at 3:55pm.
51. The ﬁgure below illustrates an isosceles right
triangle with legs of length 1, along with onefourth of a circle centered at the rightangle
vertex of the triangle. Using the result that
the shortest path between two points is a line
segment, explain why this ﬁgure shows that
2(squareroot of 2) <2

math  Reiny, Wednesday, January 25, 2012 at 5:10pm
I see this is the second time you posted this.
Of course you realize that we can't see any diagram, but I think I can draw it from your description
First of all, you must have a typo.
Did you mean 2√2 < π ??
Since your statement of2√2 < 2 is false, (2√2 = appr. 2.8)
In the triangle let the hypotenuse be h
h^2 = 1^2 + 1^2 = 2
h = √2
the arc is (1/4)(2π) = π/2
then because of the straight between two points is always less than a curve between the same two points,
√2 < π/2
multiply by 2
2√2 < π
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