| Title:
|
Krátký příběh o obecném tvaru Pythagorovy věty (Czech) |
| Title:
|
A short story on the general form of Pythagoras Theorem (English) |
| Author:
|
Dlab, Vlastimil |
| Language:
|
Czech |
| Journal:
|
Rozhledy matematicko-fyzikální |
| ISSN:
|
0035-9343 (print) |
| Volume:
|
94 |
| Issue:
|
4 |
| Year:
|
2019 |
| Pages:
|
8-15 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This article presents the following simple property of a general triangle $ABC$: Let $D$ be an arbitrary point and $A_0$, $B_0$, $C_0$ the feet of the perpendiculars from $D$ on the (possibly extended) sides $BC$, $CA$, $AB$, respectively. Then \[ |{AC}_0|^2 + |{BA}_0|^2 + |{CB}_0|^2 = |{C_0B}|^2 + |{A_0C}|^2 + |{B_0A}|^2. \] This statement is a proper generalization of the Pythagorean theorem. Surprisingly, it does not appear in textbooks or other publications. (English) |
| MSC:
|
51M04 |
| MSC:
|
97G40 |
| . |
| Date available:
|
2020-02-20T12:27:31Z |
| Last updated:
|
2021-01-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/148012 |
| . |
| Reference:
|
[1] Bečvář, J., Dlab, V.: Bohatství pýthagorejských tvrzení včetně Pythagorovy věty pro čtyři i více bodů v prostoru.Pokroky matematiky, fyziky a astronomie, 62 (2017), 4, 283–294. |
| Reference:
|
[2] Dlab, V., Williams, K. S.: The many sides of the Pythagorean theorem.The College Mathematics Journal, 50 (2019), 3, 162–172. MR 3955325, 10.1080/07468342.2019.1580527 |
| Reference:
|
[3] Kuřina, F.: 10 pohledů na geometrii.ALBRA, Praha, 1996. |
| Reference:
|
[4] Maor, E.: The Pythagorean Theorem.Princeton University Press, Princeton, 2007. MR 2316578 |
| Reference:
|
[5] van der Waerden, B.: Science awakening.Oxford University Press, New York, 1961. MR 0124984 |
| . |
