Difference between revisions of "Jadhav Theorem"
(This theorem is an Arithmetic progressions number pattern found by Jyotiraditya Jadhav. This has many uses as seen in the paper) |
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| − | + | '''Jadhav Theorem''', or '''Jadhav Arithmetic Theorem''' is an equation which is applicable for any three consecutive terms of an [[arithmetic sequence]]. This theorem is derived by [[Jyotiraditya Jadhav]]. | |
| − | Jadhav Theorem or Jadhav Arithmetic | ||
| − | Statement | + | == Statement == |
| − | |||
| + | If any three numbers <math>a</math>, <math>b</math> and <math>c</math> are taken with a constant common difference, then the difference between the square of the 2nd term (b) and the product of the first and the third term (ac) will always be the square of the common difference (d). In other words, <math>b^2-ac = d^2</math> | ||
| − | + | == Proof == | |
| − | + | From [[difference of squares]], the equation <math>b^2-d^2 = (b-d)(b+d)</math> holds. We can rewrite <math>b-d</math> and <math>b+d</math> as <math>a</math> and <math>c</math>, respectively. Now our equation is <math>b^2-d^2 = ac</math>, and rearranging gives us <math>b^2-ac = d^2</math>, as desired. | |
| − | + | == Uses == | |
| − | |||
| − | + | * This can be used to find the square of any number without a calculator. | |
| + | ** For example, let's find square of <math>102</math>. This number is part of the arithmetic series <math>100,102,104</math> with common difference <math>2</math>. Wwe can derive <math>b^2 = d^2+ac</math> from Jadhav Theorem. The square of common difference is 4 and the product of <math>a = 100</math> and <math>c = 104</math> is 10400 and later adding square of common difference (4) into it will make it 10404 and that is square of 102. | ||
| + | ** Let's find the square of 406. It is a term of arithmetic progression <math>400,406,412</math> with common difference 6. <math>400 \cdot 412</math> can be easily found as <math>164800</math>, and adding square of common difference (36) to this makes it 164836 which is square of 406. | ||
| + | * This pattern can be used to make equations for unknown quantities of the arithmetic series, as this is in a form of 4 variables then it can be used to make a equation of 4 unknown quantities with other three equations (quadratic equation). | ||
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Revision as of 14:23, 2 February 2025
Jadhav Theorem, or Jadhav Arithmetic Theorem is an equation which is applicable for any three consecutive terms of an arithmetic sequence. This theorem is derived by Jyotiraditya Jadhav.
Statement
If any three numbers 
, 
and 
are taken with a constant common difference, then the difference between the square of the 2nd term (b) and the product of the first and the third term (ac) will always be the square of the common difference (d). In other words, 
Proof
From difference of squares, the equation 
holds. We can rewrite 
and 
as and , respectively. Now our equation is 
, and rearranging gives us , as desired.
Uses
- This can be used to find the square of any number without a calculator.
- For example, let's find square of
. This number is part of the arithmetic series 
with common difference 
. Wwe can derive 
from Jadhav Theorem. The square of common difference is 4 and the product of 
and 
is 10400 and later adding square of common difference (4) into it will make it 10404 and that is square of 102. - Let's find the square of 406. It is a term of arithmetic progression
with common difference 6. 
can be easily found as 
, and adding square of common difference (36) to this makes it 164836 which is square of 406.
- For example, let's find square of
- This pattern can be used to make equations for unknown quantities of the arithmetic series, as this is in a form of 4 variables then it can be used to make a equation of 4 unknown quantities with other three equations (quadratic equation).
. This number is part of the arithmetic series 
with common difference 
. Wwe can derive 
from Jadhav Theorem. The square of common difference is 4 and the product of 
and 
is 10400 and later adding square of common difference (4) into it will make it 10404 and that is square of 102.
with common difference 6. 
can be easily found as 
, and adding square of common difference (36) to this makes it 164836 which is square of 406.This article is a stub. Help us out by expanding it.
