The Triangles of Aristarchus

2004 ◽  
Vol 97 (4) ◽  
pp. 228-231
Author(s):  
Alan W. Hirshfeld
Keyword(s):  
High School ◽  
Elementary Geometry ◽  
Lunar Eclipse ◽  
Ancient Greek ◽  
High School Geometry ◽  
The Earth ◽  
School Geometry ◽  
Greek Mathematician ◽  
Similar Triangles ◽  
First Time

The ancient Greek mathematician Aristarchus demonstrated for the first time how it was possible, using simple observations and elementary geometry, to measure distances to bodies in the solar system. Aristarchus' methods used a lunar elcipse to approximate the diameter of the Earth, and used the shadow cone of a lunar eclipse to form similar triangles and proportional measurements. The mathmatics can be easily understood by a high school geometry student.

Euclid and Descartes: A Partnership

1991 ◽  
Vol 84 (9) ◽  
pp. 706-709
Author(s):  
Dorothy Hoy Wasdovich
Keyword(s):  
High School ◽  
Euclidean Geometry ◽  
High School Geometry ◽  
School Geometry ◽  
And Algebra ◽  
First Time ◽  
Coordinate Geometry

Although Descartes developed the application of algebra to geometry over 400 years ago, his work has had little impact on the high school geometry course. Geometry and algebra are still taught as separate, unrelated subjects rather than as complementary approaches to mathematics. Any coordinate geometry that is included in a course in Euclidean geometry is apt to be placed in one chapter or unit with the implication that it is “optional” and the material covers theorems that have already been proved. If methods of proof are to be compared, why not do it the first time a theorem is encountered?

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