Geometry

The geometers of ancient Greece invented a peculiar game for themselves, a game called Construction, whose objective is to draw various geometric figures of interest. We are permitted to use just two instruments: an unmarked straightedge (a ‘ruler’), and a compass. Using these, we can draw a straight line through any given pair of points, and we can draw a circle with any given point as centre and passing through any other given point. (Oh yes, we also possess a pencil and an eraser, please do not feel worried about that!)

Shwetha Ram

When I received an email from Giridhar of Azim Premji Foundation that the forthcoming issue of W their newsletter Learning Curve was all about Mathematics, two words instantly popped into my head - Love… and… Hate! And I was pleasantly surprised when I read further on that Learning Curve would like me to narrate my (rather choppy) ride with this intriguingly abominable subject called Math.

Ask children in school which subject they dislike the most; chances are that 9 out of 10 will say A Mathematics. In fact, if you probe a little deeper, you will discover that 7 out of 10 children say they are 'terrified' or 'mortally scared' of the subject. Why children, ask any adult and you will find a similar pattern.

ne of the scarier words in a math student’s lexicon is the word locus! The definition (A path traced by a point when it moves under certain condition) seems amorphous, difficult to pin down and much too open-ended! This topic is usually introduced in high school; we are deliberately presenting problems on locus which will give students a gentler introduction to the same.

A recent paper by Bizony (2017) discussed the interesting golden ratio properties of a Kepler triangle, defined as a right-angled triangle with its sides in geometric progression in the ratio 1 : √φ : φ, where φ =  (1 + √5)/2

Fagnano’s Problem: In 1775, Giovanni Fagnano posed and solved the problem - “For a given acute angled triangle, determine the inscribed triangle of minimum perimeter.” Using calculus, Fagnano showed the solution to be the Orthic Triangle – a triangle formed by the feet of the three altitudes. A different proof was given in At Right Angles, Vol. 6, No.

For each of these three means (arithmetic mean, geometric mean and harmonic mean) , there is a simple and well-known geometric construction that illustrates it, but is there a single diagram that illustrated all three at the same time?
Euclidean Geometry is fascinating. It has captured our imagination for centuries. Many beautiful theorems have been discovered and proved, and myriad mind-boggling problems have been posed and solved, yet we haven’t got tired of  it. To the creative mind, geometry is a source of immense pleasure and contentment. We look for some more in a little-known result in plane geometry called “The Eyeball Theorem” and uncover some of its geometrical features.

 The pullout, this issue, is continued from the previous issue and is based on Geometry at the primary level. In many ways, the teaching of geometry approached in the right way holds an immense potential for learning the art of seeing and observing....

The possibility of learning mathematics through ICT support has never before been so promising.

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