Download e-book for kindle: An Elementary Course In Synthetic Projective Geometry by Derrick Norman Lehmer

By Derrick Norman Lehmer

Meant to offer, As easily As attainable, The necessities of man-made Projective Geometry - Chapters: One-To-One Correspondence - relatives among basic kinds In One-To-One Correspondence With one another - blend of 2 Projectively similar basic varieties - Point-Rows Of the second one Order - Pencils Of Rays Of the second one Order - Poles And Polars - Metrical houses Of The Conic Sections - Involution - Metrical houses Of Involutions - at the historical past of man-made Projective Geometry - Index

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Additional info for An Elementary Course In Synthetic Projective Geometry

Example text

7. Two lines u and u' revolve about two points U and U' respectively in the same plane. They go in the same direction and at the same rate of speed, but one has an angle a the start of the other. Show that they generate a point-row of the second order. PROBLEMS 39 8. Discuss the question given in the last problem when the two lines revolve in opposite directions. Can you recognize the locus? 40 An Elementary Course in Synthetic Projective Geometry FIG. 10 PROBLEMS 41 FIG. 11 [37] CHAPTER IV - POINT-ROWS OF THE SECOND ORDER 60.

As A moves along u, trace the path of B so that the two men may always see each other in the two mirrors. 4. Two boys walk along two paths u and u' each holding a string which they keep stretched tightly between them. They both move at constant but different rates of speed, letting out the string or drawing it in as they walk. How many times will the line of the string pass over any given point in the plane of the paths? 5. Trace the lines of the string when the two boys move at the same rate of speed in the two paths but do not start at the same time from the point where the two paths intersect.

For if we cut across them by a line, we obtain two projective point-rows superposed on the same straight line, which may have no more than two selfcorresponding points. The same considerations apply to two projective axial pencils which have the same axis. 52. Point-rows in perspective position 35 51. Projective point-rows having a self-corresponding point in common. Consider now two projective point-rows lying on different lines in the same plane. Their common point may or may not be a self-corresponding point.

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An Elementary Course In Synthetic Projective Geometry by Derrick Norman Lehmer

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