Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-24T14:56:32.641Z Has data issue: false hasContentIssue false
  • English
  • Français

The Hindu method for completing the square

Published online by Cambridge University Press:  01 August 2016

Dave L. Renfro
Dave L. Renfro*
Affiliation:
ACT Inc., Iowa City IA 52243-0168, USA, [email protected]
Get access Rights & Permissions [Opens in a new window]

Extract

In a September 2005 note in The Mathematics Teacher, Gordon [1] gave a variation on the method of completing the square that fraction-phobic students are likely to find easier, along with the comment: ‘This variation is so obvious it must have been discovered many times over, but I have never seen it in print and thought it would be useful to disseminate it more widely.’ The method Gordon [1] gave is to multiply by 4a, and then add b2, to both sides of ax2 + bx = −c to produce 4a2x2 + 4abx + b2 = b2 −4ac. The left side of this last equation can be factorised as (2ax + b)2, and now we have a pure quadratic whose solution is straightforward.

Type
Articles
Information
The Mathematical Gazette , Volume 91 , Issue 521 , July 2007 , pp. 198 - 201
Copyright
Copyright © The Mathematical Association 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Gordon, Warren B., Variation on completion of the square, Mathematics Teacher 99 2 (September 2005) p. 85.Google Scholar
2. Smith, David E., History of mathematics, Volumes I & II, Dover Publications (1958).Google Scholar
3. Kumar Bag, Amulya, Mathematics in ancient and medieval India, Chaukhambha Oriental Research Studies 16, Chaukhambha Orientalia (1979).Google Scholar
4. Datta, Bibhutibhusan and Narayan Singh, Avadhesh, History of Hindu mathematics: A source book, Parts I and II, Asia Publishing House, (1962q). Google Scholar
5. Hayashi, Takao, Śrīdhara’s authorship of the mathematical treatise Ganitapañcavimśt, Historia Scientiarum (2) 4 (1995) pp. 233–250.Google Scholar
6. Joseph, George Gheverghese, The crest of the peacock: non-European roots of mathematics, (2nd edn.), Princeton University Press (2000).Google Scholar
7. Kaye, G. R. and Ramanujacharia, N., The Triśatikā of Śrīdharācarya, Bibliotheca Mathematica (3) 13 (1912–13) pp. 203–217.Google Scholar
8. Ganitanand, , On the date of Śrīdhara, Ganita-Bhāratī 9 (1987) pp. 54–56.Google Scholar
9. Pingree, David, Śrīdhara, in Charles Coulston Gillispie (editor in chief), Dictionary of Scientific Biography, Volume 12, Charles Scribner’s Sons (1975) pp. 597–598.Google Scholar
10. Chrystal, George, Algebra: An elementary textbook for the higher classes of secondary schools and for colleges (7th edn.), two parts, American Mathematical Society (1999).Google Scholar
11. Hawthorne, Frank, Completing the square, Mathematics Student Journal 3 1 (February 1956) p. 1.Google Scholar
12. Sharman, H. L., The quadratic equation, Math. Gaz. 27 (October 1943) pp. 184–185.Google Scholar
13. Rietz, Henry Lewis, Crathorne, Arthur Robert, and Taylor, Edson Homer, School algebra: a first course, Henry Holt and Company (1915).Google Scholar
14. Collins, Joseph Victor, Advanced algebra, American Book Company (1911).Google Scholar
15. Milne, William J., Advanced algebra for colleges and schools, American Book Company (1902).Google Scholar
16. Wells, Webster, Advanced course in algebra, D. C. Heath & Company (1904).Google Scholar
17. Brenke, William C., Advanced algebra, The Century Company (1917).Google Scholar
18. Freund, John E., A modern introduction to mathematics, Prentice-Hall (1956).Google Scholar
19. Kogbetliantz, Ervand G., Fundamentals of mathematics from an advanced standpoint, Volumes 1 and 2, Gordon and Breach Science Publishers (1968)Google Scholar
20. Lennes, Neis J., College algebra, revised edition, Harper & Brothers Publishers (1940).Google Scholar
21. Pettit, Harvey Pierson and Luteyn, Peter, College algebra, John Wiley & Sons (1932).Google Scholar
22. Wells, E. D., Review of Pettit and Luteyn’s ‘College Algebra’, American Mathematical Monthly 40 (1933) pp. 288–289.Google Scholar
23. Youse, Bevan K., Fundamentals of mathematics, Dickenson Publishing Company (1966).Google Scholar
24. Robinson, Horatio Nelson, A theoretical and practical treatise on algebra (38th edn.), Ivison & Phinney (1859).Google Scholar