Talk:Area of a circle
Area of a circle was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake. | |||||||||||||
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addition proposal[edit]
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@CiaPan: Thank you for thinking along. I've added some extra explanation to support my theorem. Please note, that I'm not calculating , what I'm doing, is comparing the circle directly to a square, instead of other polygons. Gmac4247 (talk) 20:42, 19 January 2021 (UTC)
— Preceding unsigned comment added by Gmac4247 (talk • contribs) 08:00, 10 May 2021 (UTC) Gmac4247 (talk) 09:35, 15 May 2023 (UTC) |
Disproval of the mathematical constant pi[edit]
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The following discussion has been closed. Please do not modify it. |
The idea of the mathematical constant is based on the assumption, that the circumference of a circle can be calculated from the difference of the perimeters of an inscribed and a circumscribed polygon. To test this theory, I start with squares. r1=radius of the small circle; r3=radius of the larger circle; a=side of the small polygon; A1/P1=area/perimeter of the small circle; A2/P2=area/perimeter of the small polygon; A3/P3=area/perimeter of the larger circle; A4/P4=area/perimeter of the larger polygon; c=coefficient of the area/perimeter of the circle I continue with hexagons.
The number of the polygons' sides can be increased to infinite. Problem #1: The mathematical constant is based on calculating with 71 side polygons. Such determination is a rough guess between 4 and infinite. Problem #2: Despite of the difference decreases between the polygons' perimeter, as the number of their sides increases, the actual value of their perimeter can only be calculated with endless fractions. (See above for instance.) That means decrease of accuracy. Take the areas of the squares and the inscribed circles instead:
This proportion enables to exactly determine the area of the circle between the squares and vice versa: the square between the inscribed and the circumscribed circles. File:Find_the_area_of_a_circle_by_cutting_it_to_four_quarters.jpeg Gmac4247 (talk) 09:27, 15 May 2023 (UTC)
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History Section[edit]
The single paragraph in the history section doesn't flow logically. First it is stated that Eudoxus of Cnidus proved the area is proportional to the square of the radius. However, it is later claimed that "Prior to Archimedes, Hippocrates of Chios was the first to show that the area of a disk is proportional to the square of its diameter". But, this raises the question why Eudoxus of Cnidus was mentioned first. Indeed, Hippocrates of Chios lived a century before Eudoxus of Cnidus, so what motivates the sequencing of the paragraph?
Another, more minor issue, is that proportional to the square of the radius, versus diameter, is trivially equivalent. But it wastes the reader's mental energy when these different ways of referring to the same thing are used, since it momentarily raises the question whether there is a difference. Ajrmmm (talk) 05:08, 5 July 2022 (UTC)
Semicircle proof: bounds of integration[edit]
The first integral goes from - r to r, while the second goes from - π/2 to π/2, but when performing the trigonometric substitution, i got the integral from - x/sin θ to x/sin θ.
How do I get the same bounds given in the proof? 138.255.106.16 (talk) 14:44, 16 October 2022 (UTC)
- The text is correct as written. Citation would be nice, although this is arguably WP:CALC.
- This is not a help page for mathematics. You might try asking on a site intended for that. Or you might read a calculus textbook section on integration in polar coordinates. There's a good chance that it will contain this exact example. Mgnbar (talk) 14:58, 16 October 2022 (UTC)
Can this ref be considered valid?[edit]
Please see this addition by User:Ebony Jackson on 7 January 2014:
Is the page linked there (published at shreevatsa.wordpress.com
) a reliable source? I'm afraid it counts as a primary source and as such it should be considered WP:OR.
--CiaPan (talk) 17:05, 18 January 2023 (UTC)
- Hi CiaPan, you can remove the reference if you want. But I would leave the fact (that there is no better approximation with denominator <16604) there. The fact is routine to verify for anyone with computer literacy, so I would think it would fall under WP:CALC. Ebony Jackson (talk) 23:23, 22 January 2023 (UTC)