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"परिमिती" च्या विविध आवृत्यांमधील फरक

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(चर्चा | योगदान)
(चर्चा | योगदान)
ओळ २४: ओळ २४:
This approximation is within about 5% of the true value, so long as `a' is not more than 3 times longer than `'`b' (in other words, the ellipse is not too "squashed"):
This approximation is within about 5% of the true value, so long as `a' is not more than 3 times longer than `'`b' (in other words, the ellipse is not too "squashed"):


ellipse perimeter (approx) = 2pi into square root of [(a squared+b squared)/2]
ellipse perimeter (approx) = 2pi into square root of [(a squared+b squared)/2].


उदा० a = १०; b = ६. तर परिमिती = ५१.८१२४७३३७.(approximate).

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Approximation 2 :
Approximation 2 :


ओळ ३२: ओळ ३५:
ellipse perimeter (approx) = pi into [ 3(a+b) - square root of ((3a+b)(a+3b))]
ellipse perimeter (approx) = pi into [ 3(a+b) - square root of ((3a+b)(a+3b))]


उदा० a = १०; b = ६. तर परिमिती = ५१.०५३९७२७९.(approximate).

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Approximation 3 :
Approximation 3 :


Ramanujan also came up with this one. First we calculate "h":
रामानुजमचे सूत्र : First we calculate "h":


h = (a-b)<sup>2</sup>/(a+b)<sup>2</sup>
h = (a-b)<sup>2</sup>/(a+b)<sup>2</sup>


Then, ellipse perimeter (approx) = pi(a+b)(1 + 3h/(10+square root of (4-3h))
Then, ellipse perimeter (approx) = pi(a+b)(1 + 3h/(10+square root of (4-3h))

उदा० a = १०; b = ६. तर परिमिती = ५१.०५३९९७७३ (Most accurate)

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[[वर्ग:भूमिती]]
[[वर्ग:भूमिती]]

१८:०२, ३ एप्रिल २०१९ ची आवृत्ती

त्रिकोणाची परिमिती = तिन्ही बाजूंच्या लांबींची बेरीज

सूत्रे

आकार सूत्र सूत्रामधील चल संख्या
वर्तुळ = त्रिज्या.
त्रिकोण , आणि = त्रिकोणाच्या प्रत्येक बाजूची अनुक्रमे लांबी.
चौरस = चौरसाची बाजू
आयत = लांबी आणि = रुंदी

टीप : वर्तुळाच्या परिमितीला परीघ म्हणतात.

लंब वर्तुळाची परिमिती

a = मोठी त्रिज्या; b = छोटी त्रिज्या.

Approximation 1 :

This approximation is within about 5% of the true value, so long as `a' is not more than 3 times longer than `'`b' (in other words, the ellipse is not too "squashed"):

ellipse perimeter (approx) = 2pi into square root of [(a squared+b squared)/2].

उदा० a = १०; b = ६. तर परिमिती = ५१.८१२४७३३७.(approximate).


Approximation 2 :

The famous Indian mathematician Ramanujan came up with this better approximation:

ellipse perimeter (approx) = pi into [ 3(a+b) - square root of ((3a+b)(a+3b))]

उदा० a = १०; b = ६. तर परिमिती = ५१.०५३९७२७९.(approximate).


Approximation 3 :

रामानुजमचे सूत्र : First we calculate "h":

h = (a-b)2/(a+b)2

Then, ellipse perimeter (approx) = pi(a+b)(1 + 3h/(10+square root of (4-3h))

उदा० a = १०; b = ६. तर परिमिती = ५१.०५३९९७७३ (Most accurate)