Chapter 6 Constructions and Tilings (Class 7 - Latest Maths NCERT (Ganita Prakash II) Concept Notes)

Welcome to Chapter 6: Constructions and Tilings! This chapter blends artistic design with geometric precision, showing how complex patterns can be built from simple rules. We begin by revisiting the construction of "Eyes" to discover the Perpendicular Bisector—the mathematical line that splits a segment into two equal, perpendicular parts. By using only an unmarked ruler and a compass, you will learn to find midpoints with greater accuracy than any scale and explore historical methods from the ancient Indian Śulba-Sūtras, where mathematicians used stretched ropes to achieve perfect geometric alignment for ritual altars.

The curriculum guides you through the mastery of Angle Bisection and the essential skill of Copying Angles. These foundational techniques allow us to construct intricate figures like 8-petalled flowers, precisely parallel lines, and stunning architectural features such as Trefoil and Pointed Arches found in historical monuments like the Red Fort. You will also discover the internal logic of a Regular Hexagon, learning how six congruent equilateral triangles fit perfectly around a central point to complete a $360^\circ$ rotation without leaving any gaps.

In the final section, we dive into the world of Tiling (or Tessellation). From solving 7-piece Tangram puzzles to determining if a grid can be covered by $2 \times 1$ tiles, you will learn to use "Data Detective" logic—such as the clever black-and-white coloring strategy—to prove when a tiling is mathematically impossible. We also explore tiling in nature’s engineering, such as hexagonal bee hives, and in the mathematical art of M.C. Escher. These resources, meticulously prepared by learningspot.co, provide step-by-step construction guides and visual proofs to bridge the gap between abstract geometry and the patterns of our daily lives.