The Pythagorean theorem and some of its generalizations
Date of Publication
2002
Document Type
Bachelor's Thesis
Degree Name
Bachelor of Science in Mathematics
College
College of Science
Department/Unit
Mathematics and Statistics
Abstract/Summary
The Pythagorean Theorem relates the sides of a right triangle. The Law of Cosines is a generalization of the Pythagorean Theorem because it also relates the sides of a triangle, not necessarily a right triangle.
If a, b, c are the sides of a right triangle where c is the hypotenuse, we can put three squares with sides 1, b, c on the sides of the right triangle such that the side of length a coincides with the side of the square with side a and similarly with the squares with sides b and c. The Pythagorean Theorem states that the sum of the areas of the two smaller squares is equal to the area of the larger square. The Pythagorean Theorem can be generalized by replacing the squares with semicircles, similar triangles and more generally with proportional regions. Finally, this generalization and Law of Cosines were unified into one single formula.
Abstract Format
html
Language
English
Format
Accession Number
TU11096
Shelf Location
Archives, The Learning Commons, 12F, Henry Sy Sr. Hall
Physical Description
55 numb. leaves
Recommended Citation
Chan, S. L., & Go, E. C. (2002). The Pythagorean theorem and some of its generalizations. Retrieved from https://animorepository.dlsu.edu.ph/etd_bachelors/17229
