Example C True Shape of a Planar Figure

Example C: True Shape of a Planar Figure - Revolution of a Plane Additional Task to the multimedia book „Darstellende Geometrie/ 3 D-Geometry“, published by Veritas Educational Edition Student Edition ISBN - 978 -3 -7058 -9079 -4 ISBN - 978 -3 -7058 -9293 -4 Special edition for teachers: The print version shows handouts of theory and worked-out examples. Each handout can be printed in colour and is also suitable as a solutions handout. Through the use of animated Power. Point files it is possible to structure the lessons in a contemporary and innovative manner for students. Special edition for students: The print version consists of well prepared worksheets to start working right away. On the CD you will find colourful Power. Point presentations, including theory as well as solved examples with step-by-step explanations. This provides a highly efficient technique in developing an understanding of geometry and its concepts. for more DETAILS and ORDER 1

Example C: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! The planar polygon is given by its vertices ABCDEF. Complete the polygon in the front viewlocate missing vertices C and E: c) Α‘‘ E’’ 3’’ h 2‘‘ 1’’ Show the polygon ABCDE in the front view. D‘‘ B‘‘ 2’’ Define the true shape and size of the polygon- by revolution of a its plane about a second principle line through e. g. point E. C’’ Α‘ p 1’’= p 2’ E‘ h 2‘ 3‘ 1‘ B‘ 2‘ D‘ C‘ 2

Example C: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! Rotate the polygon about h 2. A 0’’ Α‘‘ Start to rotate e. g. point D. Δx. A E’’ 3’’ Define point A 0 and C 0 in the same way. h 2‘‘ 1’’ Δx. D D‘‘ Point B 0 can either be constructed in the same way or by FIX POINT. B‘‘ 2’’ D 0’’ B 0’’ Δx. C C’’ Α‘ C 0’’ Δx. A E‘ Δx. D p 1’’= p 2’ h 2‘ 3‘ 1‘ Δx. C B‘ 2‘ D‘ C‘ 3

Example C: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! A 0’’ Α‘‘ Show the true size and shape of polygon ABCDE. Δx. A E’’ 3’’ h 2‘‘ 1’’ Δx. D D‘‘ B‘‘ 2’’ D 0’’ B 0’’ Δx. C C’’ Α‘ C 0’’ Δx. A E‘ Δx. D p 1’’= p 2’ h 2‘ 3‘ 1‘ Δx. C B‘ 2‘ D‘ C‘ 4

Example D: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! The planar polygon is given by its vertices ABCDE. Complete the polygon in the plan and front view- locate missing vertices C and E of plane ABD. C’’ B‘‘ D‘‘ 2’’ Locate point E in the plan view. 1‘‘ h 1’’ A‘‘ E’’ Locate point C in the front view. For accuracy use parallel lines. p 1’’= p 2’ Complete the polygon in the plan and front view. Define the true shape and size of the polygon- by revolution of a its plane about a first principle line e. g. line AE. C‘ D‘ 2‘ E‘ B‘ 1‘ A‘ h 1’ 5

Example D: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! C’’ Revolve the planar polygon parallel to π1. Rotate vertex B 0 and D 0. Define point C 0 by FIX POINT. B‘‘ D‘‘ 2’’ Δz. B 1‘‘ Δz. D h 1’’ A‘‘ E’’ C 0‘ p 1’’= p 2’ C‘ D 0‘ Δz D D‘ B 0‘ 2‘ B‘ E‘ 1‘ Δz B A‘ h 1’ 6

Example D: True Shape of a Planar Figure - Revolution of a Plane Determine the true size and shape of the polygon ABCDE by revolution about a principle line! C’’ Show the true size and shape of the polygon ABCDE. B‘‘ D‘‘ 2’’ Δz. B 1‘‘ Δz. D h 1’’ A‘‘ E’’ C 0‘ p 1’’= p 2’ C‘ D 0‘ Δz D D‘ B 0‘ 2‘ B‘ E‘ 1‘ Δz B A‘ h 1’ 7