# GeoGebra

## Exploring Fractals – The GeoGebra Way

In an article published in the November 2016 issue of At Right Angles we had seen how geometrical fractal constructions lead to algebraic thinking. The article had highlighted the iterative construction processes, which lead to the Sierpinski triangle and the Sierpinski Square carpet. Further the idea of self-similarity within these fractals was reinforced through the recursive and explicit relationships between various stages of the fractal constructions.

I n the March 2017 issue, Khushboo Awasthi had described an investigation of the familiar Square Root Spiral, which had taken her along unexpected paths filled with mathematical discoveries. At the end of the article, she posed some questions for the reader to investigate and we did just that! We share our bonanza of findings with you, and as usual, the tasks are arranged from Low Floor to High Ceiling. This time, we include some investigations with the free dynamic geometry software GeoGebra; regular constructions with compass and ruler will do the job just as well!

## A Triangle Problem

Solve this: Two sides of a triangle have lengths 6 and 10, and the radius of the circumcircle of the triangle is 12. Find the length of the third side.

## Teaching Concepts of Calculus

The topic of calculus is an integral part of the senior secondary mathematics curriculum. The concepts of limits and derivatives, which form the foundation of Calculus, are often hard to teach. In this article, we suggest a dynamic way of teaching the concept of the derivative through practical examples which may be easily explored through GeoGebra applets available through the Internet.

## Conics, Paper folding, Geogebra II

In this article we shall describe the construction of the ellipse and the hyperbola using a similar strategy of paper-folding followed by a Geogebra exploration. The reader may consider the previous article as a pre-requisite to this one.

## 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.

## Of Paper Folding, Geogebra and Conics

The conics include circle, ellipse, parabola, hyperbola and a pair of intersecting lines. The first and the last can be readily drawn on paper, but there are no constructions for the remaining three using compasses and straight edge. Paper folding
(to be described presently) provided one such way to generate the three remaining conics on paper without much difficulty.

## Solution to the ‘Origamics’ Problem

In this note, we offer an explanation to the observations made in the ‘Origamics’ article (November 2013 issue of At Right
Angles).

## Folding and Mapping Turned-Up Folds

Haga’s Origamic activities require students to explore simple, geometric properties found when we fold paper in prescribed ways. The aim of these activities is to give students easy-to-explore paperfolding puzzles so that they can experience a micro-version of the three stages of mathematical research: exploration, conjecture and proof. In this article, we take up another ‘origamics’ exploration by Dr. Kazuo Haga from the chapter 'Intrasquares and Extrasquares' of his book.

## Teacher’s Diary on Classroom Assessment – II

"Assessment needs to provide answers for two questions: How is the student evolving as a learner?  What can I do to facilitate that learning? With the encouragement of a supportive principal, I re-worked the model for formative assessment..."