Understanding Point Symmetry

In the previous post, we have learned about line symmetry. In this post, we are going to learn about point symmetry, another type of symmetry.

If a figure is rotated 180 degrees about a point and it coincides with its original position, then it is said that the figure has point symmetry. The point of rotation is called the point of symmetry.

The figure below shows the point symmetric polygon ABCDEF rotated clockwise about P, its point of symmetry. The polygon outlined by the dashed line segments shows its original position.  Continue reading…

 

Understanding Line Symmetry

Many people believe that symmetry is beauty. Nature is full of symmetric objects. There are many man-made structures that are also symmetric. In this post, we are going to discuss some of the basic mathematical properties of symmetric objects. We will limit our discussion to line symmetric objects.

Line Symmetry

A figure is line symmetrical when it can be folded along a straight line such that the folded shapes fit exactly on top of each other. The fold line is called the line of symmetry.

When a symmetric figure is folded along its line of symmetry, the parts that are on top of each other are called the corresponding parts. In the polygon below with line of symmetry AB, points C and D are corresponding points, segments GB and HB are corresponding sides, and angle G and angle H are corresponding angles. Since the folded shapes fit exactly on top of each other, the corresponding angles are congruent and their corresponding sides are also congruent.  Continue reading…

 

Book Review: The Humongous Book of Calculus Problems

I bought this book a year ago as a refresher of Calculus and as of now, I am almost finished reading it. I think what separates this book from the rest are the numerous worked examples (well, 1000 of them) with detailed solutions and explanations. Additional pointers and explanations in layman’s words are provided as notes.

This book has 565 pages containing 28 chapters. The first 8 chapters contain a review about equations, polynomials, functions, and trigonometry, while the remaining chapters discussed topics in Calculus I and II: Limits, Differentiation, Integration, Parametric and Polar Equations, Sequences and Series. As a bonus, a chapter on Differential Equations is also included.  Continue reading…

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