Difference between revisions of "Construct a pentagon/construction"
(new) |
(clear float left only) |
||
Line 11: | Line 11: | ||
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. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 0 === | === Step 0 === | ||
Line 19: | Line 19: | ||
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. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 1 === | === Step 1 === | ||
Line 27: | Line 27: | ||
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. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 2 === | === Step 2 === | ||
Line 35: | Line 35: | ||
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. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 3 === | === Step 3 === | ||
Line 43: | Line 43: | ||
Draw a circle M with radius OM. | Draw a circle M with radius OM. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 4 === | === Step 4 === | ||
Line 51: | Line 51: | ||
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. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 5 === | === Step 5 === | ||
Line 59: | Line 59: | ||
Draw (two) circles with center A' and radius QA' and PA'. Find their intersections with circle O; call these B, C, D, and E. | Draw (two) circles with center A' and radius QA' and PA'. Find their intersections with circle O; call these B, C, D, and E. | ||
− | <br clear=" | + | <br clear="left" /> |
=== Step 6 === | === Step 6 === |
Revision as of 12:18, 23 June 2006
Contents
Construction: Inscribed Pentagon
Given a circle, inscribe a regular 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 radius 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.