NCERT Solutions for Class 5th Maths Chapter 7 Stitching a design on 24 points, and the flower of circles — Circle Designs
Book page 101 Updated on2026-09-19
Q1.
Look at the circle given below. It is marked with points 1 to 24. Join points 1 to 11, 11 to 2, 2 to 12, and so on till you reach back at 1. (Try it with different coloured threads on a thick paper or cloth.)
Answer
Keep repeating two moves: jump forward 10 points, then go back 9 points. After 48 straight lines you arrive back at point 1 and the design is complete.
Read the rule from the numbers given
1 to 11 — that is a jump forward of 10.
11 to 2 — that is a jump back of 9.
2 to 12 — forward 10 again.
12 to 3 — back 9 again.
So the order is: 1, 11, 2, 12, 3, 13, 4, 14, 5, 15 … and it keeps going.
When you pass 24, start counting from 1 again — the numbers run round the circle. Every pair of moves shifts you forward by just one point, so after 24 pairs (that is 48 lines) you are back at 1.
All 48 straight lines drawn. The eye sees a curved star, but every single line is straight.
Points on the circle = 24 Each pair of moves (+10 then −9) shifts the start by 1 To come back to point 1 you need 24 such pairs Lines drawn = 24 × 2 = 48
Why the design looks curved: Not one of the 48 lines is curved. But their ends move round the circle in a steady way, and the edges of so many straight lines together trick the eye into seeing smooth curves. Designers call this “curve stitching”.
Doing it with thread: Push a pin through each of the 24 points on thick paper. Take a needle and coloured thread, and sew 1 to 11, then 11 to 2, and so on. Change the colour after every 12 stitches for a lovely effect.
Q2.
Can you think of a way to make a design exactly like the image given here? Try to make it.The design given in the book, page 101.
Answer
Yes. Draw five circles, all of the same size — one in the middle, and four more with their centres on the middle circle. Keep your compass opened to the same width the whole time.
Steps
Open your compass to any width you like. Do not change it again.
Draw the middle circle. Mark its centre O.
Draw two diameters through O that cross at a right angle, like a plus sign. They meet the circle at four points — call them top, bottom, left and right.
Put the compass point on the ‘top’ point and draw a full circle. Do the same on the bottom, left and right points.
Look at the middle. Four petal shapes have appeared, all meeting at O.
Colour it. Petals one colour, the bulging outer pieces another, the little corner pieces a third.
The green circle is the first one. The four cream circles are centred on its top, bottom, left and right points.
Why the petals appear: Two circles of the same size that overlap share a lens-shaped piece. Here every pair of neighbouring circles overlaps in exactly that way, and because all four new circles pass through the centre O, all four petals meet neatly at O.
Keep going: Do not change the compass, and draw more circles centred on the points where circles cross. You get the pattern that decorates temple walls and rangoli floors all over India.