Probably more than any other Mathematical theorem, the Pythagorean Theorem, has been credited with having numerous proofs including those of Algebraic proofs and Geometric proofs some of which date back thousands of years.
The Pythagorean Theorem can be generalized in many ways such as:
Higher dimensional spaces to spaces that are not Euclidean, to objects that are not right angles and certainly not least, to objects that are not triangles at all, but n-dimensional solids.
While sounding very impressive, Robert Ollis himself once an exceptionally high achieving Math Student (awarded Straight Distinctions in Pure Mathematics in 1970) understands completely, that while most students appreciate that a 2 ..b 2 ..c they don’t grasp the geometrical concepts involved.
Yet, with more than 35 years tutoring experience, Robert Ollis also knows, that it is by far much easier for students to understand the Pythagorean Theorem from a geometrical sense without resorting, to algebra. Hence the clarification made whenever introducing any new student to Pythagoras Theorem.
We are in fact talking about 3 areas when we state:
Robert Ollie makes a further distinction in that, for the Pythagorean Theorem to work, it needs triangles that have a right angle … there simply must be a 90 angle as is demonstrated in the diagram below.
Furthermore, Robert Ollis assists his students in their understanding of the topic, with the following tips:
A. The Hypotenuse is the longest side and is opposite the right angle
B. To find the largest area….ADD
C. To find the smallest area SUBTRACT
Robert Ollis knows that when students know how to apply and understand the relationship between the shapes and sizes that exist as well as having the knowledge of how to deal with measurements and the relationships of lines, angles, surfaces and solids, they will be much better prepared and more confident to use them in their everyday lives.
Yet, while the extensive use of the Pythagorean Theorem and its many proofs generally seen as being restricted to the very specialized fields such as Engineering, Architecture, Construction, Surveying and the like, the theorem is also used by Scientists, Chemists, Physicians, Electricians, Farmers, Carpenters and Landscapers.
Hence the need very early on, for High School students to fully grasp the Pythagorean Theorem and its many applications before making the all important career decisions that can either limit or enhance their quality of life in future years.
If you the student, parent or teacher, would like to know more about what Robert Ollis and RobertOMath.com can do and how he continues to enhance the math results of hundreds and hundreds of his math students, then click on the links below for more information.