NCERT Solutions for Ganita Prakash (Part 2) Chapter 4 Exploring Some Geometric Themes
Updated on 2026-09-05
About this chapter
A fractal is a self-similar shape: it contains smaller copies of itself, over and over. Ferns, trees, coastlines, lightning and the towers of the Kandariya Mahadev Temple at Khajuraho all show this. The Sierpinski Carpet keeps 8 of every 9 sub-squares at each step, so R n = 8 n squares remain, H n = (8 n − 1)⁄7 holes have appeared, and the remaining area is (8⁄9) n — shrinking towards 0. The Sierpinski Gasket keeps 3 of every 4 triangles: 3 n triangles remain, (3 n − 1)⁄2 holes have been cut, and the area left is (3⁄4) n . The Koch Snowflake replaces every side by four sides one-third as long. So it has 3 × 4 n sides of length (1⁄3) n , and a perimeter 3 × (4⁄3) n that grows without limit — an unbounded boundary around a bounded region. A net is a solid unfolded flat. A cube has 11 nets, a
- .1 Fractals
- Sierpinski Gasket
- Koch Snowflake
- –774.2 Visualising Solids
- Making Solids
- –81Nets of a cube
- Nets of other solids
- Nets of a cylinder and a cone
- The octahedron and the dodecahedron
- –85Shortest Paths on a Cube
Exercises
- .1 Fractals — In-text Questions Page 714
- .1 Fractals — In-text Question Page 724
- Sierpinski Gasket — Figure it Out Page 72
- Koch Snowflake — Figure it Out Page 73
- –774.2 Visualising Solids — Build it in Your Imagination Page 75
- Making Solids — In-text Questions Page 79
- Making Solids — In-text Questions Page 80
- –81Nets of a cube — Figure it Out Page 80
- Nets of other solids — In-text Questions Page 81
- Nets of a cylinder and a cone — In-text Questions Page 82
- The octahedron and the dodecahedron — In-text Questions Page 83
- –85Shortest Paths on a Cube — In-text Questions Page 84
- –87Shortest Paths on a Cube — In-text Questions Page 86
- –91Representation of Solids on a Plane Surface — In-text Questions Page 89
- –93Front view, top view and side view — Figure it Out Page 92
- Shadows — In-text Questions Page 94
- –97Views of solids built from cubes — Figure it Out Page 95
- –100Isometric Projections and isometric drawing — In-text Questions Page 97
- –102Drawing on Isometric Grids — Figure it Out Page 100