Example Cup Truncated Cone with Circles of 3

Example: Cup – Truncated Cone with Circles of 3 rd Edge View 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: Cup – Truncated Cone with Circles of 3 rd Edge View A cup is formed by a truncated cone, which is given in the profile view. Its top and basement circle show third edge view. Complete the front view of the truncated cone, which is given by its rotational axis. Construct all outline points of the truncated cone exactly. Locate midpoints M 1‘‘ and M 2‘‘. In the profile view all radii of cone´s circles and its height show true length. In the front view the cone´s circles are imaged as ellipses. Each major axis shows true length and is perpendicular to rotational axis of cone. p 3‘‘ = p 2‘‘‘ a‘‘‘ Use folding lines to locate according points on the minor axis. M 2‘‘‘ Define each ellipse by circles of curvature. M 1‘‘‘ M 1‘‘ 2

Example: Cup – Truncated Cone with Circles of 3 rd Edge View A cup is formed by a truncated cone, which is given in the profile view. Its top and basement circle show third edge view. Complete the front view of the truncated cone, which is given by its rotational axis. Construct all outline points of the truncated cone exactly. Define outline points (and outline generatrices) of the cone. Use sphere, which touches cone along top circle. Determine outline of sphere in the profile view. Define outline of sphere in the front view. p 3‘‘ = p 2‘‘‘ a‘‘‘ N 2‘‘ M 2‘‘‘ M 1‘‘ 3

Example: Cup – Truncated Cone with Circles of 3 rd Edge View A cup is formed by a truncated cone, which is given in the profile view. Its top and basement circle show third edge view. Complete the front view of the truncated cone, which is given by its rotational axis. Construct all outline points of the truncated cone exactly. Show according outline circle u of the sphere in the profile view. Remember: The outline of each solid must always be perpendicular to respective lines of sight. Define intercepts of outline circle and cone´s basement circle. These intercepts are required outline points in the front view. p 3‘‘ = p 2‘‘‘ Locate outline points in the front view. u‘‘ a‘‘‘ N 2‘‘‘ U 1, 2‘‘‘ s 2‘‘‘ a‘‘ N 2‘‘ M 2‘‘‘ U 1‘‘ U 2‘‘ u‘‘‘ M 1‘‘ 4

Example: Cup – Truncated Cone with Circles of 3 rd Edge View A cup is formed by a truncated cone, which is given in the profile view. Its top and basement circle show third edge view. Complete the front view of the truncated cone, which is given by its rotational axis. Construct all outline points of the truncated cone exactly. Construct outline points of the cone on the smaller circle, either by same idea of construction by a sphere or by similar triangles. Remember: intersection curves of a cone by parallel planes must be similar. p 3‘‘ = p 2‘‘‘ a‘‘‘ N 2‘‘‘ U 1, 2‘‘‘ s 2‘‘‘ u‘‘ a‘‘ N 2‘‘ M 2‘‘‘ U 1‘‘ U 2‘‘ u‘‘‘ M 1‘‘ U 3‘‘ U 4‘‘ 5

Example: Cup – Truncated Cone with Circles of 3 rd Edge View A cup is formed by a truncated cone, which is given in the profile view. Its top and basement circle show third edge view. Complete the front view of the truncated cone, which is given by its rotational axis. Construct all outline points of the truncated cone exactly. In the front view the outline generatrices of the truncated cone go through respective outline points U 1, U 2 and U 3, U 4. They must also be tangent lines of each ellipse. Show proper visibility. p 3‘‘ = p 2‘‘‘ u‘‘ a‘‘‘ N 2‘‘‘ U 1, 2‘‘‘ s 2‘‘‘ M 2‘‘‘ U 1‘‘ U 2‘‘ u‘‘‘ M 1‘‘ U 3‘‘ U 4‘‘ 6