circle

I write this to tell myself that it was not a dream...

This year I taught a bunch of fifth standard kids in Sahyadri School KFI (Krishnamurti Foundation India), who, like all others of their age, were high-energy kids; they were willing to explore but found it difficult to sit down in one place. I had a great relationship with them. The air in the classroom was of love, trust and wonder!

Websites and focus interest groups are a good source for interesting problems. But it’s rarely that one gets down to solving these; more often they go into a to-do list. We hope that the solution presented here will encourage you to try more of these. Look at the steps of the process: Visualization, definition of the problem, connection to known formulas and then good old mathematical processing. Problem solved!

The approximation of π is a popular pastime of students of mathematics and I have started with the familiar age-old way, of fitting a regular polygon tightly in a circle of radius r. The vertices of the n-sided polygon are joined to the centre of the circle so that the angle subtended at the centre by each segment is 360/n. If n is sufficiently large, the perimeter of the polygon approaches the circumference 2πr of the circle and this approximation improves as the number of segments increases.

These are excellent GeoGebra exercises for students helping them to develop and practise skills of visualisation, logical sequencing, making connections and recalling theory. Read on.

Introduction to circle and its parts and how they are interlinked - a Shikshamitra resource.

Find the solution to the circle area problem posed in the earlier issue of AtRiA.

This time the Low Floor, High Ceiling series focuses on regular polygons inscribed in circles.

 

Can a Circle be a Polygon?

Explanation:

How many sides does a circle have?

A circle could have: 1 curved side! or infinite sides (each side being very small) or no sides.

Problems ahead, solve them.

The Pythagorean theorem tells you how beautifully the baby circle is quarter the size of its parents! Check it for yourself.

 

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