deerghavrutt

deerghavrutt kaarteeya nirdeshaank system me .

ganit me deerghavrutt ek esa shaankav hota hai jiski utkendrata ikaai se kam hoti hai. ek anya paribhaasha ke anusaar deerghavrutt kisi ese bindu ka bindupath hai jiski do nishchit binduon se doori ka yog achar rahata hai. nishchit binduon ko deerghavrutt ki naabhiyaaain (en:Focus) kehte hain. maana jaata hai ki pruthvi sahit kai grah soorya ke chaaron or ek deerghavrutteeya kaksha par ghoomate hain aur is deerghavrutt ki ek naabhi par sooraj avasthit hota hai.

anukram

jyaamiteeya visheshataaeain

deerghavitt ke do akshon mein se bade ko pradhaan aksh kah sakte hain. donon naabhi pradhaan aksh par avasthit hote hain aur deerghavrutt par sthit kisi bhi bindu ki in donon naabhiyon se doori ka yog is pradhaan aksh ki lanbaai ke baraabar yaani hamesha niyat hota hai.

deerghavrutt ka kshetrafal

deerghavrutt ka kshetrafal is sootr dvaara nikaala ja sakta hai - $A=\pi ab.$ $A=\pi ab.$

yahaaain a aur b deerghavrutt ke do akshon ke aadhe hain. yadi deerghavrutt ka sameekaran is roop mein ho $Ax^{2}+Bxy+Cy^{2}+1=0$ $Ax^{2}+Bxy+Cy^{2}+1=0$ ,

to iska kshetrafal hoga: ${\frac {2\pi }{\sqrt {B^{2}-4AC}}}$ ${\frac {2\pi }{\sqrt {B^{2}-4AC}}}$ .

paridhi

iski ganana jatil hoti hai aur iska koi saral tatha sateek sootr naheen hai. haalaaainki bhaarateeya ganitjnya raamaanujan dvaara sujhaae gaye is sootr ko saralatam tatha sateekatam maana ja sakta hai:

$C\approx \pi \left[3(a+b)-{\sqrt {(3a+b)(a+3b)}}\right]=\pi (3(a+b)-{\sqrt {10ab+3(a^{2}+b^{2})}})$ $C\approx \pi \left[3(a+b)-{\sqrt {(3a+b)(a+3b)}}\right]=\pi (3(a+b)-{\sqrt {10ab+3(a^{2}+b^{2})}})$

inhein bhi dekhein

deerghavruttalekhi
paravalaya
ati paravalaya