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Virahanka numbers kya hain?

Short mein jawab

Virahanka numbers 1, 2, 3, 5, 8, 13, 21, 34, … chhote (ek beat) aur lambe (do beat) syllables ki rhythms ginte hain. Har number apne pichhle do numbers ka jod hai. Virahanka ne ye niyam lagbhag 700 CE mein diya, Fibonacci se lagbhag 500 saal pehle, isliye inhe Virahanka–Fibonacci numbers kehte hain.

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Kavita se aaye numbers

Maths mein bahut kam sequences itne mashhoor hain jitna 1, 2, 3, 5, 8, 13, 21, 34, …, aur ye kala, science aur prakriti mein dikhta hai. Hairaani ki baat ye hai ki ye pehle kala, yaani kavita, ke zariye khoja gaya. Prakrit, Sanskrit, Marathi, Malayalam, Tamil, Telugu aur kai doosri Bhartiya bhaashaaon mein kavita ka har syllable ya to chhota hota hai ya lamba. Lamba syllable chhote se theek doguna samay leta hai, isliye kavita gaate waqt chhota syllable ek beat aur lamba do beat leta hai. Kaviyon ne ek swaabhaavik sawaal poochha: maan lo 8 beats ki line ko chhote aur lambe syllables se kitne tareekon se bhara ja sakta hai? Numbers ki bhaasha mein, 8 ko 1 aur 2 ke jod ke roop mein kitne tareekon se likh sakte hain?

Rhythms ginna

Chhote se shuru karo. Ek beat sirf ek chhota syllable ho sakta hai: 1 tareeka. Do beats 1 + 1 ya 2 ho sakte hain: 2 tareeke. Teen beats: 1 + 1 + 1, 1 + 2 aur 2 + 1, yaani 3 tareeke. Chaar beats ke 5 tareeke hain aur paanch beats ke 8. Sab ki list banaana jaldi thakaa deta hai, isliye hamein samajhdaar tareeka chahiye.

1 se 5 beats ke liye chhote aur lambe beats ki rhythms: 1, 2, 3, 5 aur 8 tareeke
Chhote aur lambe beats ki rhythms

Virahanka ka niyam

Har rhythm ya to chhote syllable (1 +) se shuru hoti hai ya lambe (2 +) se. Agar 1 + se shuru ho, to baaki hissa ek beat kam ki rhythm hai; agar 2 + se, to do beat kam ki. Isliye 5-beat rhythms = 5 chaar-beat rhythms mein se har ek ke aage “1 +” aur 3 teen-beat rhythms mein se har ek ke aage “2 +”: 5 + 3 = 8. Isi tarah 6 beats ki 8 + 5 = 13 rhythms hain. Sequence ka har number apne pichhle do numbers ka jod hai: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, … Isliye 8 beats ki line 34 tareekon se bhari ja sakti hai.

Virahanka ka niyam: paanch-beat rhythms 1 + chaar-beat rhythm ya 2 + teen-beat rhythm hain, 5 + 3 = 8, aur 233 tak ka sequence
Virahanka ka niyam

Lamba itihaas

Mahaan Prakrit vidwaan Virahanka ne ye tareeka lagbhag 700 CE mein bataaya, aur use, sahi dhang se, ek Prakrit kavita ke roop mein likha. Ve pehle jaane-maane vyakti hain jinhone ye numbers aur unhe banaane ka niyam saaf likha, Sanskrit vidwaan Pingala ke pehle ke kaam se prerna lekar, jo lagbhag 300 BCE mein the. Virahanka ke baad Gopala (lagbhag 1135 CE) aur Hemachandra (lagbhag 1150 CE) ne bhi inke baare mein likha. Pashchim mein inhe Fibonacci numbers kehte hain, ek Italian ganitagya ke naam par jinhone 1202 CE mein, Virahanka ke lagbhag paanch sadi baad, inke baare mein likha, yaani Fibonacci inke baare mein likhne waale chauthe bhi nahi the. “Virahanka–Fibonacci numbers” naam se sab is sequence ko pehchaan lete hain.

Timeline: Pingala lagbhag 300 BCE, Virahanka lagbhag 700 CE, Gopala lagbhag 1135 CE, Hemachandra lagbhag 1150 CE aur Fibonacci 1202 CE
In numbers ke baare mein kisne likha?

Sequence mein odd aur even

Numbers ek parity pattern maante hain: 1 odd, 2 even, 3 odd, 5 odd, 8 even, 13 odd, 21 odd, 34 even, … Kyunki odd + even = odd, even + odd = odd aur odd + odd = even, pattern odd, even, odd hamesha dohraata hai, aur har teesra number, yaani 2nd, 5th, 8th, …, even hota hai. Isliye bina jode keh sakte hain ki 233 aur 377 ke baad ka number even hai (vo 610 hai), aur 20th number even hai (vo 10946 hai).

Pehle 20 Virahanka numbers odd ya even ke nishaan ke saath: doosre se shuru karke har teesra even hai
Virahanka numbers ki parity

Prakriti mein, aur seedhiyon par

In numbers ko dekhne ki shaayad sabse anokhi jagah prakriti hai: daisy phool mein aksar 13, 21 ya 34 pankhudiyan hoti hain. Yahi ginti roz ki paheliyan bhi hal karti hai. Agar Angaan 8 seedhiyon waali seedhi ek ya do seedhi ek saath chadhta hai, to kisi bhi seedhi par uska aakhri kadam ek ya do seedhi neeche se aata hai, isliye har seedhi tak pahunchne ke tareeke 1, 2, 3, 5, 8, 13, 21, 34 hain: upar pahunchne ke 34 tareeke.

13, 21 aur 34 pankhudiyon waale teen daisy phool
Daisy ki pankhudiyan aksar Virahanka numbers hoti hain

Ye kyun zaroori hai

Virahanka numbers dikhaate hain ki kala, science aur maths kitne gehre jude hain, aur ye aage ki classes mein phir aayenge. Yahan ka parity wala tark parity: odd aur even se aata hai, aur ek aur tarah ki number paheli magic square kya hai mein hai. Har sawaal ka jawaab Chapter 6 ke NCERT solutions mein hai; poore Chapter 6 ke notes bhi dekho.

Practice karo

  1. Chhote aur lambe syllables se 6 beats ki kitni alag rhythms ban sakti hain?

    1. (a) 8
    2. (b) 11
    3. (c) 13
    4. (d) 21
    Jawab dekho

    Jawab: (c) 13

  2. Virahanka sequence mein 89 ke baad kaunsa number aata hai?

    1. (a) 134
    2. (b) 144
    3. (c) 178
    4. (d) 155
    Jawab dekho

    Jawab: (b) 144

  3. Virahanka ne in numbers ka niyam lagbhag kab diya?

    1. (a) 300 BCE
    2. (b) 700 CE
    3. (c) 1202 CE
    4. (d) 1900 CE
    Jawab dekho

    Jawab: (b) 700 CE

  4. 5-beat rhythms ki ginti 5 + 3 kyun hai?

    Jawab dekho

    Jawab: Har 5-beat rhythm ya to chhote syllable aur uske baad 4-beat rhythm (5 tareeke) se shuru hoti hai, ya lambe syllable aur uske baad 3-beat rhythm (3 tareeke) se, isliye 5 + 3 = 8.

  5. Bina jode batao, 233 aur 377 ke baad ka number odd hai ya even?

    Jawab dekho

    Jawab: Even. 233 aur 377 dono odd hain, aur odd + odd = even; sach mein 233 + 377 = 610.

Students ke sawal

Virahanka numbers kya hain?

Ye numbers 1, 2, 3, 5, 8, 13, 21, 34, 55, … hain, jinmein har number apne pichhle do numbers ka jod hai. Ye un rhythms ko ginte hain jo ek beat ke chhote syllables aur do beat ke lambe syllables se ban sakti hain: jaise, 5 beats 8 tareekon se bhare ja sakte hain.

Virahanka–Fibonacci numbers kisne khoje?

Ye pehle Bhartiya kavita ke vidwaanon ke kaam mein aaye. Pingala ne, lagbhag 300 BCE mein, aisi rhythms ka adhyayan kiya; Virahanka ne lagbhag 700 CE mein ek Prakrit kavita mein numbers banaane ka niyam diya; aur Gopala (lagbhag 1135 CE) aur Hemachandra (lagbhag 1150 CE) ne inke baare mein likha. Fibonacci ne Italy mein 1202 CE mein likha.

Prakriti mein Virahanka numbers kahan dikhte hain?

Ek mashhoor udaaharan phool hain: daisy mein aksar Virahanka number jitni pankhudiyan hoti hain, jaise 13, 21 ya 34. Ye numbers kala, science aur maths mein bhi dikhte hain, kavita aur dhol-vaadan se lekar chitrakala aur imaaraton tak.

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