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The Frontiers of Society, Science and Technology, 2020, 2(15); doi: 10.25236/FSST.2020.021518.

Further Exploration of Pythagorean Theorem


Haohan Zhang, Junbao Liang

Corresponding Author:
Haohan Zhang

Experimental school affiliated with Zhuhai no.1 high school, Zhuhai, 519000, China


Pythagorean theorem was raised by Pythagoras in 551 BC, and it was also proposed in an even more ancient time by a Chinese mathematician called Shang Gao in the 11th century BC, although this process is not well-known. Moreover, it is one of the most famous theories, almost all of us have studied in our middle schools. The Pythagorean theorem tells us the relationship between three sides of a right triangle, that is, a2+b2=c2. However, mathematics is developing all the time, obviously, this theorem is not enough for us to explore in a higher dimension, and we are also interested in some equations with specific numbers. In this essay, we will focus on four questions, to generalize the Pythagoras theorem into three dimensions and discuss both rational and irrational solutions.


Pythagorean Theorem, stereographic projection, modular arithmetic

Cite This Paper

Haohan Zhang, Junbao Liang. Further Exploration of Pythagorean Theorem. The Frontiers of Society, Science and Technology (2020) Vol. 2 Issue 15:152-159. https://doi.org/10.25236/FSST.2020.021518.


[1] Eli Maor, The Pythagorean Theorem: A 4,000-Year History, Princeton University Press, (2019), pp. 11-12.
[2] José William Porras Ferreira, Pythagorean Triples, https://www.researchgate.net/
publication/322255294_Pythagorean_Triples, January 2018/ 7th September 2020.