At Right Angles, pen, paper and armchair – what more do you need for these rainy days? The November 2021 issue will keep you absorbed for days. Keep reading!

Beyond Four Walls — Contain a mathematician in a room and you can be sure that some thinking on quadrilaterals will happen! Our second issue during the pandemic has much to keep you absorbed and happily engaged with problems- of the mathematical kind. From age digit reversals to an algorithm for evacuating a room — there is material for every age group. We begin with the all important question: Why Should You Study Mathematics? And we also carry a review of the Classes I‑III Sikkim Mathematics Textbooks, the development of which our URC-PDP played such a key role in. Do revert with your feedback on AtRiA.​editor@​apu.​edu.​in

AtRiA, November 2019 focuses on journeys ‑some are enjoyable, some tiresome, some endless. A mathematician’s journey is full of unexpected delight, simply because of unexpected detours, sudden discoveries and interesting alternatives. Have fun as you travel with us. Read all about the young Yatris and their journey of discovery in Features. This section also describes more abstract journeys from the Regular Pentagon to the Icosahedron and the Dodecahedron (Part 2) and from the familiar 2 and 3 dimensions to n dimensions in Extension of the Pythagorean Theorem. In ClassRoom, Simple Cryptography and Triangles with Integer Sides are articles sparked off by previous articles in AtRiA . An Unusual Proof of the Centroid Theorem, Modified Pascal Triangle and Orthocentre of a Triangle may motivate you to write similarly! You will find ideas in our regular columns – How to Prove It, Low Flow High Ceiling and TechSpace which features the simulation of a dice game this time. Our issue is short of 100% without the PullOut, enjoy the learning trajectory on Percentages, defined and illustrated with plenty of examples in this issue. How Craig Barton Wishes he’d Taught Maths is an excellent review by Sir Timothy William Gowers, reprinted from his Weblog.

1. State of Working India 2019 is being published close on the heels of the 2018 report. The principal reason is that this year’s report aims to intervene in the debate over employment generation in time for the general elections to be conducted in April and May 2019. In this report we present an update on the jobs situation for the period between 2016 and 2018, and also present some ideas for employment generation.

2. The recent controversy over employment statistics should be seen in the context of the fact there is now a fully established politics of unemployment in India. This is a new development that needs to be understood. The politics of unemployment is typically a feature of middle-to-high income countries, not low-to-middle income countries. Traditionally, the principal economic issue of broad spectrum political significance in India has been poverty, not unemployment.

3. There have been some new developments, which when juxtaposed with older structural and cultural factors, can account for why this is happening in India, a lower middle income country with a per capita GDP one third that of China and half that of Indonesia. The ​‘precocious’ part of the Indian labour market that resembles higher income countries, that has always been there to a limited extent, is now substantial and rapidly rising, and more to the point, it has spread throughout the country, including the rural areas. This has laid the material basis for a widespread politics of unemployment.

4. Without any claim to being a complete list, we discuss seven key factors on the supply side of the labour market and two crucial demand side factors that together contribute to the crisis. On the supply side we have high growth rates and aspirations, the youth bulge, the education wave, the dominance of ​‘general’ degrees, sub-standard degrees, and continued relevance of caste and gender based rigidities. On the demand side we have the collapse of public sector employment and inability of the private sector to create adequate good jobs due to contractualisation and automation.

5. The foregoing factors are clear to all observers of the Indian economy. The question is, of course, what can be done? Several long-term and short-term measures which face these structural conditions as they exist currently, are needed. Public action and spending should be strong elements of all these measures.

6. The report details four policy measures for addressing the crisis. In Chapter Three, Strengthening Towns through Sustainable Employment: A Job Guarantee Programme for Urban India, we propose a programme that calls for providing 100 days of guaranteed work at D500 a day for a variety of works in small towns. It also provides for 150 contiguous days of training-and-apprenticeship at a stipend of D13,000 per month for educated youth. In Chapter Four, Creating Good Jobs through a Universal Basic Services Programme, we argue that a well-executed UBS would go a long way in restoring public goods to their rightful place in society, creating decent work in the process. Chapter Five, How to Revive Indian Manufacturing: On the Need for Industrial Policy, by Jayan Jose Thomas discusses the renewed interest in, and continued relevance of industrial policy. Srinivas Thiruvadanthai in Chapter Six, Using Fiscal Policy to Alleviate the Job Crisis, argues that there is ample fiscal space to address the criss via public spending.

7. India is at a crucial juncture in its economic development where timely public investment and public policy can reap huge rewards. At the same time, being in denial about the current realities and missing this window of opportunity can have large negative consequences in social and economic terms. Let us act together to ensure that it is the first eventuality that comes to pass.

The November issue has beaten the nay-sayers at their own game with articles that celebrate the joy of doing mathematics through games, stories, applications of mathematics and activities on line and in the classroom. 

The word ​‘heuristics’ has always left me fumbling for the perfect definition. Rule of thumb seems adequate but too informal, as a teacher trainer, I’ve always preferred to illustrate rather than define this word. And the first article in the November issue does just that- Gaurav Bhatnagar, leads you gently into the Exponential Series- a heuristic definition! The relaxed tone continues with V. G. Tikekar setting the stage to arrive at formulae which are usually given and proved using mathematical induction. He, on the other hand, uses the narrative mode to set the context which explains and then proves the sum of squares and sum of cubes formulae. From story we move to song, V. Ramprashanth’s article Tonic Ambiguity is a delightful depart from our usual articles and it explains very simply, using just the concepts of ratios, how two hearers can place the same tones at different positions on the musical scale. CoMaC and then Shailesh Shirali, wrap up the Features section with a bouquet of proofs.

ClassRoom opens with Prithwijit De’s trademark investigative style – the title simply says A Triangle Problem – read on to find out more. Student Corner is our happy space and this time, we have Vinay Nair’s students talking about Happy Numbers and Bodhideep Joardar Investigating Pi. Next, we have Naveen Yadav combining Set Theory, Geometry and Combinatorics in Scalene Triples and Ujjwal Rane follows up on his previous article on Fagnano’s Theorem with a very visual, very practical alternative proof. A video of this result has also been uploaded by him on YouTube, it is available at https://​youtu​.be/​5​M​r​N​M​-​VxXd8. Low Floor High Ceiling features a modification of an investigation into triangles having the same area and perimeter and conditions for congruency. Learn about G numbers in Hara Gopal’s article. We’re particularly delighted to bring in yet another new sub-section to ClassRoom – Course Correction features vignettes from pedagogical experience, ways in which pitfalls leading to misconceptions can be addressed and used to advantage to strengthen student understanding. This time, we feature the solution of a problem from a traditionally ambivalent topic- Combinatorics.

On to TechSpace, we have not one but two articles this time. Thomas Lingefjard describes the use of technology to introduce concepts in Calculus and Sangeeta Gulati describes changes in the Desmos software and how it can now be used to build activity kits. Problem Corner is a treasure trove of interesting problems in addition to the usual Middle School, Senior School and Adventures in Problem Solving articles.

Review features an old classic – R. Ramanujam takes us through a lovely guided tour of Hardy’s A Mathematician’s Apology. And there is an unexpected bonanza, with this issue, we will feature a mini- review, it may be of a video clip, a game, a story…………..all things mathematical in essence. This time, J. Shashidhar talks about Marcus du Sautoy’s Story of Mathematics. Read the facing page to know more about this fascinating mathematician.

Pullout has graduated to Upper Primary – with this issue, we bring you a compendium of information about teaching Integers- surely the point when students begin to have negative thoughts about mathematics. I’m sure you’ll enjoy reading how to combat those tendrils of fear.

Two themes dominate this issue of AtRiA: Archimedes & Magic Squares — an unlikely combination! Both are exceedingly rich topics to write about, with histories that go far back in time. Who can’t be both charmed and thrilled by the story of Archimedes?

Explore ​‘Inter-disciplinary Science’ with 5 articles that connect knowledge, methods, & perspectives from across the natural sciences. Trace the exciting history of familiar science concepts in ​‘Serendipity’ & ​‘Annals of History’. Enjoy reading about the quirky & brilliant J.B.S Haldane in ​‘Biography of a Scientist’. Re-discover the wonders of the world within us (Macrophages) & in outer space (Mars Orbiter Mission) in our section ​‘In here/​Out there’. Prepare to be surprised by the colourful life of the humble fly in the section on ​‘Nature in your Backyard’. Check out our ​‘Science Online’ section for a step-by-step introduction to an open access software tool for understanding Time. Also enjoy our pull-out posters on ​‘Experiments with Water’ & ​‘Ten things you didn’t know about – Blood’!

In this issue of the Learning Curve, Jean Dreze talks about the beneficial aspects of the Mid-day Meal Scheme and the Spastics Society of Karnataka elaborates on the accommodations and modifications required to integrate children with special needs into mainstream schools.

In this issue of the Learning Curve, teacher absence in India, one of the Education system’s most insistent problems, is discussed and observations from Chinese Mathematics Classrooms are documented for their potential to serve as lessons for India.