Prakriti ka Pasandeeda Kram

Class 7 Maths · Chapter 6: Number Play · NCERT Ganita Prakash section 6.4

Seekho

Sanskrit, Prakrit aur kai Bharatiya bhashaon mein kavita mein chhote akshar (1 thaap) aur lambe (2 thaap) hote hain. Kaviyon ne poocha: theek n thaap bharne wali kitni layein? Ye n ko 1 aur 2 ke jod mein likhne jaisa hai: 3 = 1 + 1 + 1 = 1 + 2 = 2 + 1, yaani 3 tareeke.

n = 1, 2, 3, 4: 1, 2, 3, 5 ways

Chatur tareeka: har 5-thaap lay 1 + (4-thaap lay) ya 2 + (3-thaap lay) se shuru hoti hai. To tareeke(5) = tareeke(4) + tareeke(3) = 5 + 3 = 8, aur tareeke(6) = 8 + 5 = 13. Har number pichhle do ka jod: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 …

8 = 5 + 3 · 13 = 8 + 5

Prakrit vidvaan Virahāṅka ne ye niyam lagbhag 700 CE mein diya, Piṅgala (lagbhag 300 BCE) se prerit hokar; baad mein Gopala aur Hemachandra ne likha. Pashchim mein inhe Fibonacci numbers kehte hain, 1202 CE ke ek lekhak ke naam par, lagbhag 500 saal baad. Isliye Virahāṅka–Fibonacci numbers.

Pattern: parity odd, even, odd, odd, even, odd, odd, even … har 3 par dohraati, to 20va number even (20 = 3 × 6 + 2, sthaan 2 jaisa). Prakriti mein daisy mein aksar 13, 21 ya 34 pankhudiyan. Aur 8 seedhiyan 1 ya 2 karke chadhne ke 34 tareeke!

O, E, O, O, E, O, O, E …

Explore: 4 banaane ke saare tareeke.

1. 4 ko 1 aur 2 ke jod mein likhne ka har tareeka tap karo.

Yaad rakho

• n thaap ki layon (1 aur 2 ke jod) ki ginti nva Virahāṅka number.
• Har Virahāṅka number pichhle do ka jod: 1, 2, 3, 5, 8, 13 …

Quick check

Lagaataar do Virahāṅka numbers 987 aur 1597. Aage kya?

1. 2584
2. 2207
3. 610
4. 2594

Socho

7 ko 1 aur 2 ke jod mein likhne ke kitne tareeke?

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.