Thales' Theorem
Thales’ Theorem
Thales’ Theorem simply states that if three points exist within a circle, and one of those points is the diameter of the circle, then the resulting triangle will always be a right triangle. This simple idea can become very useful for certain applications such as, identifying the center of a circle with its converse. On the triangle the vertex of the right angle always terminates at the ends of the diameter line. By locating the two points of the diameter line and drawing a line connecting them, the center can be found directly between them. This is the case if and only if it is a right triangle. Thales’ theorem is a special case of the inscribed angle theorem. It was attributed to Thales of Miletus and proved in the third book of Euclid’s Elements, 33rd proposition. According to history the Indian and Babylonian mathematicians knew this for special cases prior to Thales. It is even said that he learned of inscribed triangles during his journey to Babylon. It is mostly attributed to him due to his initial proving, utilizing his results of Isosceles base angles being equal and the total sum of angles within a triangle equally 180 degrees. Thales’ is the subject of two stories regarding astronomy and geometry. In the first, he predicted an eclipse in the year 585 BCE. In the next, Thales took observations from two land points and used his knowledge of geometry to determine the distance of a ship. Despite his contribution to the mathematic community regarding Isosceles triangles and the sum of angles within a triangle, Thales’ Theorem remains his most noteworthy accomplishment.
References
Bogomolny, A. (1996-2014). Munching on Inscribed Angles. Retrieved from http://www.cut-the-knot.org: http://www.cut-the-knot.org/pythagoras/Munching/inscribed.shtml
Bogomolny, A. (1996-2014). Thales ' Theorem. Retrieved from http://www.cut-the-knot.org/: http://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/ThalesTheorem.shtml
Dehaan, M. (2011, June
Thales’ Theorem simply states that if three points exist within a circle, and one of those points is the diameter of the circle, then the resulting triangle will always be a right triangle. This simple idea can become very useful for certain applications such as, identifying the center of a circle with its converse. On the triangle the vertex of the right angle always terminates at the ends of the diameter line. By locating the two points of the diameter line and drawing a line connecting them, the center can be found directly between them. This is the case if and only if it is a right triangle. Thales’ theorem is a special case of the inscribed angle theorem. It was attributed to Thales of Miletus and proved in the third book of Euclid’s Elements, 33rd proposition. According to history the Indian and Babylonian mathematicians knew this for special cases prior to Thales. It is even said that he learned of inscribed triangles during his journey to Babylon. It is mostly attributed to him due to his initial proving, utilizing his results of Isosceles base angles being equal and the total sum of angles within a triangle equally 180 degrees. Thales’ is the subject of two stories regarding astronomy and geometry. In the first, he predicted an eclipse in the year 585 BCE. In the next, Thales took observations from two land points and used his knowledge of geometry to determine the distance of a ship. Despite his contribution to the mathematic community regarding Isosceles triangles and the sum of angles within a triangle, Thales’ Theorem remains his most noteworthy accomplishment.
References
Bogomolny, A. (1996-2014). Munching on Inscribed Angles. Retrieved from http://www.cut-the-knot.org: http://www.cut-the-knot.org/pythagoras/Munching/inscribed.shtml
Bogomolny, A. (1996-2014). Thales ' Theorem. Retrieved from http://www.cut-the-knot.org/: http://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/ThalesTheorem.shtml
Dehaan, M. (2011, June
References: Bogomolny, A. (1996-2014). Munching on Inscribed Angles. Retrieved from http://www.cut-the-knot.org: http://www.cut-the-knot.org/pythagoras/Munching/inscribed.shtml Bogomolny, A. (1996-2014). Thales ' Theorem. Retrieved from http://www.cut-the-knot.org/: http://www.cut-the-knot.org/Curriculum/Geometry/GeoGebra/ThalesTheorem.shtml Dehaan, M. (2011, June 13). The Proof and Practice of Thales’ Theorem for Circled Triangles. Retrieved from http://www.decodedscience.com: http://www.decodedscience.com/the-proof-and-practice-of-thales-theorem-for-circled-triangles/1250 Friedrich, T., & Agricola, I. (2008). In T. Friedrich, & I. Agricola, Elementary Geometry (p. 50). Heath, T. (1921). In T. Heath, A History of Greek Mathematics:From Thales to Euclid (p. 131). Oxford. Reference, M. O. (2009). Thales ' Theorem. Retrieved from http://www.mathopenref.com/: http://www.mathopenref.com/thalestheorem.html (Retrieved 05/06/2014). In P. &. D.Patsopoulos, The Theorem of Thales: A Study of the naming of theorems in school Geometry textbooks. Patras University.