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Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property
K. Idicula Koshy1
Section:Research Paper, Product Type: Journal-Paper
Vol.11 ,
Issue.1 , pp.1-5, Feb-2024
Online published on Feb 28, 2024
Copyright © K. Idicula Koshy . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: K. Idicula Koshy, “Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.11, Issue.1, pp.1-5, 2024.
MLA Style Citation: K. Idicula Koshy "Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property." International Journal of Scientific Research in Mathematical and Statistical Sciences 11.1 (2024): 1-5.
APA Style Citation: K. Idicula Koshy, (2024). Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property. International Journal of Scientific Research in Mathematical and Statistical Sciences, 11(1), 1-5.
BibTex Style Citation:
@article{Koshy_2024,
author = {K. Idicula Koshy},
title = {Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2024},
volume = {11},
Issue = {1},
month = {2},
year = {2024},
issn = {2347-2693},
pages = {1-5},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3420},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=3420
TI - Ellipse Perimeter Approximation: Two High Accuracy Formulae Derived From a Perimeter Property
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - K. Idicula Koshy
PY - 2024
DA - 2024/02/28
PB - IJCSE, Indore, INDIA
SP - 1-5
IS - 1
VL - 11
SN - 2347-2693
ER -
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Abstract :
There is no simple formula for the exact perimeter of an ellipse; but there are several formulae giving approximate value of the perimeter. However, some of them fail to give the correct perimeter for degenerate ellipse; some others, though simple, provide very low accuracy level. In this research article the author introduces two high accuracy formulae derived from a geometric property of the elliptic arc in the first quadrant. Both these formulae are applicable to ellipses of all aspect ratios and the absolute relative error yields are less than one centimeter per kilometer.
Key-Words / Index Term :
Ellipse, Aspect Ratio, Perimeter, Simpson’s Rule, p-norm, Absolute Relative Error, ppm.
References :
[1] Erwin Kreiszig, ‘Advanced Engineering Mathematics’ Ch. 17; Wiley, 2010.
[2] Gerard P Michon, ‘Perimeter of an ellipse: A Review’, Weblink: Numericana
[3] K.I. Koshy, ‘A new Approx. Formula by a new Approach’ IJESIRD, July, Vol.6, Issue.1, pp.1-6, 2019.
[4] K. Idicula Koshy, ‘Ellipse Perim. Approx. by p-norm formula’, BOMSR, Vol.11, Issue.4, pp.93-97, 2023.
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