#### At Right Angles March 2017

 The Art of the Matter - can a picture be a powerful pedagogical tool? At Right Angles believes it can, and if you read the write up on the facing page, I'm sure you will agree with us. Going to the heart of the art is key to mathematics and there's more of the same inside this issue. We begin with Ramya Ramalingam, a sixteen year old school girl, unraveling the mysteries of Knot Theory for us. And Haneet Gandhi picks up where her series on Tessellations stopped, with a facinating article on tiling and the pictures we can create with different combinations and permutations of polygons.In the ClassRoom section, Khushboo Awasthi opens up the Square Root Spiral with a series of investigative questions; Ujjwal Rane proves Fagnano's Theorem in several innovative ways. CoMaC describes an unusual way to bisect an angle and also manages to pull yet another 3-4-5 triangle which has long connected math with art pops up in Kepler's triangle - read more about it in Marcus Bizony's article. And in How To Prove It, Shailesh Shirali uses Ptolemy's theorem to reveal all kinds of facinating relationships in cyclic quadrilaterals.         Download Pdf version TechSpace features the first part of a two part series on constructive definitions; Michael de Villiers shows you how to do so with a GeoGebra activity centered on the golden rhombus. Truely cutting edge math pedagogy!Our review this time is by Kamala Mukunda who shares her views on Liping Ma's classic Knowing and Teaching Elementary Mathematics. This is a must-have for every school library and a must-read for mathematics teachers of all classes. Finally, it's Time - this PullOut by Padmapriya Shirali will give you several new ideas to introduce this all important concept and help students quantify something which impinges on their consiciousness long before they come to school. We hope you enjoy this issue - do share your thoughts with us on AtRia.editor@apu.edu.in or our FaceBook page AtRiUM.
###### Features
 Ramya Ramalingam Tying it up, without loose ends Knot Theory Addendum Haneet GandhiCataloguing Uniform Tiling
###### In the Classroom
 Ujjwal RaneFagnano's Problem Shailesh shiraliFagnano's Problem addendum Marcus BizonyThe Golden Ratio, unexpectedly Sneha Titus and Swati SircarDADs Rule! Khushboo AwasthiSpiral of Square Roots CoMaCAngle Bisection CoMaC3 4 5 strikes again A. RamachandranCongruence & Constructibility in Triangles Shailesh ShiraliInequalities in Algebra & Geometry 1 Shailesh ShiraliHow to Prove It

###### Problem Corner

 Sneha Titus & Arthmaraman RProblems for the Middle School Prithwijit De & Shailesh ShiraliProblems for the Senior School CoMaCTWO Problem Studies

###### Pullout

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