The Circle: A Mathematical Exploration Beyond the Line by Alfred S. Posamentier & Robert Geretschläger

Author:Alfred S. Posamentier & Robert Geretschläger [Posamentier, Alfred S. & Geretschläger, Robert]
Language: eng
Format: epub
Tags: Geometry, Algebraic, Mathematics, Topology
ISBN: 9781633881679
Google: trbrCgAAQBAJ
Amazon: 1633881679
Publisher: Prometheus Books
Published: 2016-08-22T16:00:00+00:00

Fig. 8.2.

Using the technique above, we can construct a line segment whose measure is n times the measure of any given line segment, where n = 1, 2, 3, 4,…. We can show this in figure 8.3 by continuing the doubling of line segment AB. This will allow us to create line segments that are three times, four times, five times, etc., as long as segment AB.

As shown in figure 8.3, we will have segments multiple times as long as segment AB. We do this as follows. We draw (E, AB) to intersect (D, AB) at point F; then we draw (F, AB) to intersect (E, AB) at point G; then we could continue this process with (G, AB) to intersect (F, AB) at point H; then (H, AB) to intersect (G, AB) at point I; then (I, AB) to intersect (H, AB) at point J; and then (J, AB) to intersect (I, AB) at point K. If the reader has done these constructions beyond where figure 8.3 stopped, then he or she could note that this process can then continue indefinitely. Notice also how, while creating this construction, we were able to place many points on the line AB, which was one of our considerations for creating the line AB with countless many points.

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