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August 11, 2020

How to Pursue Mathematics after High School?

For Students who are passionate for Mathematics and want to pursue it for higher studies in India and abroad.

Let's learn how to calculate the geometric mean. This is a concept video useful for Mathematics Olympiad and ISI and CMI Entrance.

Watch and Learn:

Read and Learn: What is the Geometric mean of two numbers a and b & how to calculate it?

Suppose a and b are positive numbers then their geometric mean is defined as square root of a times b. This is the formula of geometric mean.

formula to calculate geometric mean

We will construct the geometric mean of a and b geometrically. So, here are the steps:

  1. Let's start by drawing the diameter of a circle.
  2. Suppose the two endpoints are X and Y of the diameter.
  3. Choose any point M on this particular diameter
  4. Now, let's construct a perpendicular at M which hits the circle at N.
  5. M divides the diameter into two parts XM and YM. Suppose, the length of XM and YM be a and b respectively.
  6. Now, we want to show that the length of MN is the square root of a times b, i.e., the geometric mean of a and b.
geometric mean of a and b

7. Now, join XN and YN, and then look at the triangles YMN and XMN and try to show that these two triangles are actually similar. Now, see the following proof:

Similarity proof of two triangles

8. Since, we know that similar triangles have proportional sides. So, we can say,

geometric mean proof

Hence, this is proved.

Hope you liked it!

Our Math Olympiad Program

What to do to shape your Career in Mathematics after 12th? 

From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here:

  • What are some of the best colleges for Mathematics that you can aim to apply for after high school?
  • How can you strategically opt for less known colleges and prepare yourself for the best universities in India or Abroad for your Masters or Ph.D. Programs?
  • What are the best universities for MS, MMath, and Ph.D. Programs in India?
  • What topics in Mathematics are really needed to crack some great Masters or Ph.D. level entrances?
  • How can you pursue a Ph.D. in Mathematics outside India?
  • What are the 5 ways Cheenta can help you to pursue Higher Mathematics in India and abroad?

Want to Explore Advanced Mathematics at Cheenta?

Cheenta has taken an initiative of helping College and High School Passout Students with its "Open Seminars" and "Open for all Math Camps". These events are extremely useful for students who are really passionate for Mathematic and want to pursue their career in it.

To Explore and Experience Advanced Mathematics at Cheenta
Register here

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