Difference between revisions of "Construct a pentagon/construction"
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[[Image:5star-04-finished.png|200px]] | [[Image:5star-04-finished.png|200px]] | ||
''Given a circle, inscribe a regular pentagon.'' | ''Given a circle, inscribe a regular pentagon.'' | ||
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| + | == Construction: Inscribed Pentagon == | ||
[[Image:5star-05-given.png|400px|left]] | [[Image:5star-05-given.png|400px|left]] | ||
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Although we generally consider the circle as given, in theory we should always start with two given (arbitrarily chosen) points. | Although we generally consider the circle as given, in theory we should always start with two given (arbitrarily chosen) points. | ||
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=== Step 0 === | === Step 0 === | ||
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Given points A and O, draw circle O with radius AO and diameter AA'. Let AO be 1 unit. | Given points A and O, draw circle O with radius AO and diameter AA'. Let AO be 1 unit. | ||
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=== Step 1 === | === Step 1 === | ||
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Construct the perpendicular bisector of AA' and find one intersection with circle O; call this S. | Construct the perpendicular bisector of AA' and find one intersection with circle O; call this S. | ||
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=== Step 2 === | === Step 2 === | ||
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Construct the perpendicular bisector of SO and find its intersection with line SO; call this M. | Construct the perpendicular bisector of SO and find its intersection with line SO; call this M. | ||
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=== Step 3 === | === Step 3 === | ||
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Draw a circle M with radius OM. | Draw a circle M with radius OM. | ||
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=== Step 4 === | === Step 4 === | ||
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Draw a line through A' and M. Find its intersections with circle M; call these P and Q. | Draw a line through A' and M. Find its intersections with circle M; call these P and Q. | ||
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=== Step 5 === | === Step 5 === | ||
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[[Image:5star-11-step-05.png|400px|left]] | [[Image:5star-11-step-05.png|400px|left]] | ||
| − | Draw (two) circles with center A' and | + | Draw (two) circles with center A' and radii QA' and PA'. Find their intersections with circle O; call these B, C, D, and E. |
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=== Step 6 === | === Step 6 === | ||
Latest revision as of 23:41, 1 October 2007
Given a circle, inscribe a regular pentagon.
Contents
Construction: Inscribed Pentagon
Although we generally consider the circle as given, in theory we should always start with two given (arbitrarily chosen) points.
Step 0
Given points A and O, draw circle O with radius AO and diameter AA'. Let AO be 1 unit.
Step 1
Construct the perpendicular bisector of AA' and find one intersection with circle O; call this S.
Step 2
Construct the perpendicular bisector of SO and find its intersection with line SO; call this M.
Step 3
Draw a circle M with radius OM.
Step 4
Draw a line through A' and M. Find its intersections with circle M; call these P and Q.
Step 5
Draw (two) circles with center A' and radii QA' and PA'. Find their intersections with circle O; call these B, C, D, and E.
Step 6
Draw lines AB, BC, CD, DE, and EA.
I say the figure ABCDE is a regular pentagon. QEF.
