Two Approaches to Trigonometry

Trigonometric Functions

Trigonometry is the study of the relationships between angles and sides of a triangle. This is the way it is introduced in secondary classes. The basic idea here is to use the concept of "similarity" of two triangles in a slightly formalized way and use it for practical applications like "heights and distances".

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Two Problems from IIT-JEE

IIT-JEE (Joint Entrance Examination for admission to Indian Institutes of Technology) is the most prestigious examination at 10+2 level in India. The questions are supposed to be tough and require ingenuity on the part of the student. There is a booming ecosystem of books, coaching classes and correspondence classes around IIT-JEE. But I find this ecosystem to be quite detrimental in improving the abilities of the student.

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Gauss and Regular Polygons: Conclusion

The Central Result

This is the concluding post in this series and we aim to prove the following result (proved in part by Gauss and finally the converse by Wantzel):
A regular polygon of $ n, n > 2$ sides can be constructed by Euclidean tools if and only if $ \phi(n) = 2^{k}$.

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