Double Cusp

Double cusp It is common experience that milk pot shows beautiful double cusp. It is formed by parallel or nearly parallel rays. These rays get reflected on the cylindrical surface. The bundled rays shows white cusp pattern on the surface of milk. In this applet the rays in the form of vectors are shown when number of rays is small. Thereafter only lines are shown. This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com Construction – This is done in GeoGebra. A semicircular arc is drawn. Hatching is drawn by taking a sequence of points at 5o interval on arc and drawing small line segments at 45o . from these points. Sequence of number of rays starting from a point on right and meeting mirror is drawn. The normal to mirror is drawn at each point. The reflected rays are now drawn. Number of rays is taken to be small to start with, for user to see and understand the reflection. Number now is increased to get beautiful cusp pattern. Sequence command is back-bone of this construction. Address your queries to vasantbarve@gmail.com Dr Vasant Barve, 11 September 2014, Created with GeoGebra

Kaleidoscope

Kaleidoscope  This is a toy based on the principle of multiple reflections in a pair of mirrors. Three rectangular glass strips aspect ratio of about 6 are arranged to form an equilateral triangle by the lengths abutting each other. One end is closed by a triangular glass piece. One more triangular glass piece is arranged at small distance and some colored glass pieces and beads are placed in the gap of two triangular glass pieces. Now the arrangement is wrapped in paper to hold tight together. Viewed from other end one observes beautiful patterns. Slight movement changes the patterns. At three corners hexagonal patterns are formed This is a Java Applet created using GeoGebra from www.geogebra.org - it looks like you don't have Java installed, please go to www.java.com  Construction – One need consider object, three primary images, six secondary images and three tertiary images. Thus Object + 12 images are drawn. Beyond these one has images but are faint and hence not drawn. Start with a triangle containing objects. GeoGebra has inbuilt function for reflections of object about a line. Complete all the reflections. The objects have been provided with a control point to move the object. By moving object one can make pattern change from one beautiful to next. Address your queries to vasantbarve@gmail.com Dr Vasant Barve, 11 September 2014, Created with GeoGebra