Clairaut explained triangle angle sum
- Author:
- Arthur Lee
The following figure is made to explain how the angles within a triangle may vary in order to deduce the constant angle sum property. The explanation is given by Alexis Clairaut in his book, Elements of Geometry (published in 1741). Follow the link below or open the attached pdf to read part of the book.
If you move C away from A, what happens to the size of angle C? How about angle B?
What do you notice about the change in angle C compared with the change in angle B?
Read Clairaut's book (p.35-38) in the Internet Archive:
https://archive.org/details/elementsgeometr00claigoog/page/n62/mode/2up
Alexis Clairaut's Elements of Geometry p.35-38
Hyewon Chang and Barbara Reys have written an article in the Mathematics Teaching in the Middle School, an NCTM journal (Vol. 19, No.5, Dec 2013/Jan 2014), explaining Clairaut's "historic-genetic approach" and how it is compatible with dynamic geometry tools nowadays to support students' conceptual understanding before learning to prove formally in geometry. The title of the article is "If Only Clairaut had Dynamic Geometric Tools". The article includes this example about observing and reasoning about changes of angles in a triangle.
(access this article online via HKU Library)