Shapes aur number sequences

Class 6 Maths · Chapter 1: Patterns in Mathematics · NCERT Ganita Prakash section 1.6

Seekho

Shape sequences aksar number sequences se judi hoti hain. Regular polygons ki sides gino: 3, 4, 5, 6 … 3 se shuru counting numbers. Corners bhi yahi numbers dete hain, kyonki har side ek corner par khatam hoti hai jahan se agli side shuru hoti hai.

Complete graphs ki lines gino: 0, 1, 3, 6, 10 … triangular numbers! Kyon? Naya point pehle se maujood har point se judta hai. K5 mein naya point 4 nayi lines (coral) jodta hai.

0 + 1 + 2 + 3 + 4 = 10 lines

Stacked squares mein 1, 4, 9, 16 chhote squares hain: square numbers, kyonki bade square mein n lines mein n chhote squares hain.

4 × 4 = 16

Stacked triangles se bhi 1, 4, 9, 16 milte hain! Har line gino: 1, 3, 5, 7 triangles. Ye odd numbers hain, aur odd numbers ka jod square number hota hai.

1 + 3 + 5 + 7 = 16 = 4 × 4

Koch snowflake: har step par har line segment 4 chhote segments ban jaata hai. To segments 3, 12, 48, 192 … yaani 3 guna 4 ki powers.

3 → 12 → 48 → 192 (× 4 each step)

Explore: chhote squares aur triangles jodkar bade banao, aur ek snowflake ugao.

1. 16 chhote squares se ek bada square banao.
2. 9 chhote triangles se ek bada triangle banao.
3. Koch snowflake ko 48 sides tak ugao.

Yaad rakho

• Regular polygons ki sides: 3, 4, 5 … (3 se counting numbers).
• Complete graphs ki lines: 0, 1, 3, 6, 10 … (triangular numbers).
• Stacked squares aur stacked triangles: 1, 4, 9, 16 … (square numbers).
• Koch snowflake ke segments: 3, 12, 48 … (3 × 4 ki powers).

Quick check

6 points, har point baaki har point se juda. Kitni lines?

1. 12
2. 15
3. 18
4. 30

Socho

Har regular polygon ke corners gino. Kya sides wali hi sequence milti hai? Kyon?

Practice

Teen levels (easy, medium, hard) ke naye sawaalon se practice karo, kuch hands-on, hints aur hal ke saath. Topic poora karne ke liye pichhle 5 mein se 4 sahi karo.