At a recent trade fair in the Wohascum Convention Center, an inven- tor showed a device called a "trisector," with which any straight line segment can be divieded into three equal parts. However a customer approached the inventor and said, "I need to find the midpoint of a segment, not the points 1/3 and 2/3 of the way from one end of the segment to the other!" The inventor replied, “I'm sorry, I hadn't realized there was a market for that. I suppose you will have to get a compass and use the usual high-school geometry construction."
At a recent trade fair in the Wohascum Convention Center, an inven- tor showed a device called a "trisector," with which any straight line segment can be divieded into three equal parts. However a customer approached the inventor and said, "I need to find the midpoint of a segment, not the points 1/3 and 2/3 of the way from one end of the segment to the other!" The inventor replied, “I'm sorry, I hadn't realized there was a market for that. I suppose you will have to get a compass and use the usual high-school geometry construction."
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:9. At a recent trade fair in the Wohascum Convention Center, an inven-
tor showed a device called a "trisector," with which any straight line
segment can be divieded into three equal parts. However a customer
approached the inventor and said, "I need to find the midpoint of a
segment, not the points 1/3 and 2/3 of the way from one end of the
segment to the other!"
The inventor replied, "I'm sorry, I hadn't realized there was a market
for that. I suppose you will have to get a compass and use the usual
high-school geometry construction.”
Show that the inventor was wrong. That is, show how to construct the
midpoint of any given segment using only an (unmarked) straight edge
(but no compasses) and the "trisector." Hint: Review your high-school
geometry concerning the properties of the medians of a triangle.
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