GeoGebra application : I recently found, when engaging in visualization process, if we express the hypotenuse r of a right triangle, as the area of a rectangle, with conventional sides , length l and breadth b, then one of the legs x is given as the rectangular area, whose length is determined by (l - 2) and breadth (b) and the other leg y is given as the rectangular area, whose length is squareroot of (l - 1) and breadth (2b).
Dear Mr. Koshy!
You raised a critical issue. We need apply concepts in context so we gain deeper understanding, still I argue that nobody ever would reach an absolute understanding on the Pythagorean Theorem:
1) Interviews: Savin-Baden, M., MacKenzie, A. Finding and Creating Spaces of Innovation. Postdigit Sci Educ (2021). https://doi.org/10.1007/s42438-021-00266-0, Free access: Article Finding and Creating Spaces of Innovation
2) Jabin Deguma et al. (2021). An Analogical Investigation of the Pythagorean Triangle: From a Mathematical Figure to an Ethical Praxis, Academic Journal of Interdisciplinary Studies 10(1):373, January 2021, Free access: Article An Analogical Investigation of the Pythagorean Triangle: Fro...
3) Figure 1. and Figure 2. Application of Pythagoras' theorem into two dimensional spaces. in Md. Nur Alam Siddik (2020). Economic stimulus for COVID-19 pandemic and its determinants: evidence from cross-country analysis, Heliyon 6 (2020) e05634, Free access: Article Economic stimulus for COVID-19 pandemic and its determinants...
Yours sincerely, Bulcsu Szekely
The Pythagorean theorem has fascinated people for nearly 4,000 years; there are now more than 300 different proofs, including ones by the Greek mathematician Pappus of Alexandria (flourished c. 320 CE), the Arab mathematician-physician Thābit ibn Qurrah (c. 836–901), the Italian artist-inventor Leonardo da Vinci(1452–1519), and even U.S. Pres. James Garfield (1831–81).
https://www.britannica.com/science/Pythagorean-theorem
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