Question

Can someone please give me the history of arithmetic progression? Links also appreciated.

Answer 1

http://www.math10.com/en/algebra/arithmetic-progression.html

Answer 2

if u have any doubt after reading this ....tell me thn

Answer 3

Oh I know about AP! I am studying about it! I am doing a project on it and needed info on its discovery.

Answer 4

you need the history or proof also

Answer 5

just history. What did you mean by proof?

Answer 6

theres a theory on this

Answer 7

Harvey Dubner and Tony Forbes discovered it. Any idea on how or history?

Answer 8

To derive the above formula, begin by expressing the arithmetic series in two different ways:

S_n=a_1+(a_1+d)+(a_1+2d)+\cdots+(a_1+(n-2)d)+(a_1+(n-1)d)
S_n=(a_n-(n-1)d)+(a_n-(n-2)d)+\cdots+(a_n-2d)+(a_n-d)+a_n.
Adding both sides of the two equations, all terms involving d cancel:

\ 2S_n=n(a_1 + a_n).
Dividing both sides by 2 produces a common form of the equation:

S_n=\frac{n}{2}( a_1 + a_n).
An alternate form results from re-inserting the substitution: a_n = a_1 + (n-1)d:

S_n=\frac{n}{2}[ 2a_1 + (n-1)d].
Furthermore the mean value of the series can be calculated via: S_n / n:

\overline{n} =\frac{a_1 + a_n}{2}.
In 499 AD Aryabhata, a prominent mathematician-astronomer from the classical age of Indian mathematics and Indian astronomy, gave this method in the Aryabhatiya (section 2.18).

Answer 9

are you talking about this derrivation

Answer 10

no i wasnt talking about derivation. I was talking about who and how and was their any incidents which led to the discovery of a chapter in maths called arithmetic progression.

Answer 11

According to Mathworld, which has a link in the article, an arithmetic series is the sum of an arithmetic progression or sequence. Charles Matthews has obscured this distinction by redirecting arithmetic series to arithmetic progression. I'm not sure whether the distinction made by Mathworld is commonly recognised by mathematicians, so I'm not going to revert the change. I'll wait for comments. -- Heron 15:12, 7 Mar 2004 (UTC)

The redirect only implies that information on arithmetic series is contained in the arithmetic progression article, not that the two terms are synonymous. The article is quite clear on the latter point (and mathworld is right, of course). -- Arvindn 15:39, 7 Mar 2004 (UTC)
Yes, the article has both definitions; I don't see anything obscure about it.

Charles Matthews 15:59, 7 Mar 2004 (UTC)

How about merging series&progression articles as it's done with the geometric series&progression?

I strongly think arithmetic series should be merged back into this article. Fredrik | talk 14:20, 19 August 2005 (UTC)
Fredrik, thanks! Oleg Alexandrov 19:35, 20 August 2005 (UTC)
No problem :) - Fredrik | talk 19:38, 20 August 2005 (UTC)
Mathworld includes several Egyptian math entries. A small number are my own. My view is Mathworld editors stress modern number theory conversions of rational numbers to non-concise unit fraction series, often to awkward versions of the greedy algorithm, thereby being of little value to new readers wanting to know how to read the historical Egyptian fraction rational numbers, and associated formulas. —Preceding unsigned comment added by Milogardner (talk • contribs)

Does this have anything to do with the contents of our article on arithmetic progressions? If not, it shouldn't be here. —David Eppstein (talk) 19:02, 16 September 2010 (UTC)
Of course it does. The first known arithmetic progression in the Western Tradition was written in the Kahun Paprus around 1900 BCE and again in the Rhind Mathematical Papyrus in problems 40 and 64. The formulas that found the largest and smallest terms in two different arithmetic progressions were algebraically related, and not algorithmic. The two formulas looked very much like Gauss' childhood story of summing seccessive additions of 1 to 100 by finding 50 pairs or 101, obtaining 5050. Egyptians did much better. Milogardner (talk) 19:26, 16 September 2010 (UTC)

Answer 12

read thelast paragraph

Answer 13

Thats a start. Thanks!
If you find more, please share!

Answer 14

yeah there is not much link

Answer 15

you gave me two medals???

Answer 16

you deserve it!