# ratio

## Ratio - At Right Angles Pullout

How does one introduce a topic like ratio, which is so widely present in daily life and so intimately connected with human experiences? Our cherished cultural achievements are permeated with it: music is full of ratios, as is art. Our daily existence involves cooking and shopping, and these are filled through and through with the usage of ratio. Shadows, which are present with us all through the day, offer a visual depiction of ratios in action.

## A Triangle Area Problem

Interesting problem on area and triangle.

## π Enters the 5th Class

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!

## QUILTING Explorations by a Mathematics Teacher

I must confess that it was the top layer that attracted me to quilting. This was clearly a case of the whole being greater than the sum of its parts- I was wonderstruck at how scraps of material could be pieced together to make beautiful patterns that were all at once eye-catching and pleasing.

## Arsalan’s Amazing Area Problems

On the Facebook page (AtRiUM: At Right Angles, Us and Math) linked to this magazine, one of our contributors, Arsalan Wares, has been astonishingly prolific in posting problems. A good many of these have had to do with regular hexagons; more specifically, with the areas of polygonal regions drawn within such hexagons. It is both astonishing and pleasing to see such a rich diversity of problems arising from this simple and familiar structure.

## 3,4,5 And other memorable triples Part III

In the 3rd part of the series, we are trying to find all triples (a, b, c) of coprime positive integers satisfying the property a2 = b(b + c). What solutions does the equation have (in coprime positive integers) other than (a, b, c) = (6, 4, 5)?

## How to Prove it?

In this article, we offer a second proof of the triangle-in-a-triangle theorem, using the principles of similarity geometry. Then, using vectors, we prove a result which is a generalisation of that theorem.

## When does it have Maximum Area? ~ A GeoGebra Exploration

Use GeoGebra to check when will a rectangle have maximum area when it is inscribed in a triangle.

## How to Prove It

In this article we examine how to prove a result obtained after careful GeoGebra experimentation. It was featured in the March 2015 issue of At Right Angles, in the ‘Tech Space’ section.

## Keeping Things in Proportion

‘Low Floor High Ceiling’ activities are simple age-appropriate tasks which can be attempted by all the students in the classroom. The complexity of the tasks builds up as the activity proceeds so that each student is pushed to his or her maximum as they attempt their work. There is enough work for all, but as the level gets higher, fewer students are able to complete the tasks.

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