Reading bicycle tracks

You might have come across real life accounts of how a seasoned hunter can read the pug-marks of animals and figure out surprising amount of information from them, quite Sherlock Holmes style. Now move this scenario to the concrete jungle and consider the case where you are given track marks of a bicycle wheels, can you figure out which way was the bicycle moving?

In the book “Genius at Play”, a biography of John Conway, Siobhan Roberts discusses an interesting problem. For one of the classes, Conway and his co-teachers rode bicycles on large rolls of paper and handed out the resulting tracks to the students to analyze and figure out which way the bicycle moved.

There is an easy algorithm to answer the question, which has to do with curvature of the tracks and drawing tangents and measuring distances along them.

Notice that the track made by the front wheel always has a larger curvature because when a turn is being made by the front wheel, the back-wheel is free to move only along the direction of the bicycle.

If you draw a tangent to a point P on the track made by the back-wheel of the bicycle, then the direction of the tangent shows the direction of the velocity of the back-wheel. Since this velocity is along the direction of the bicycle frame, if one moves along the tangent, there has to be a point on the outer (front-wheel) track which is exactly at the distance between the two contact points of the wheel. Thus the direction along the tangent in which the distance between the contact point P (on the inner curve) and the point on the outer curve Q stay the same, no matter which point P you choose, is the direction of motion of the bicycle.

Agony and Ecstasy of Mathematics

There are two kinds of people in the world, those who enjoy mathematics and those who don’t. What is interesting is that even those who enjoy mathematics don’t quite agree on how should mathematics be taught. On one side there are people like the famous mathematician John Conway who would carry fruits and vegetables to the classroom to teach students about geometry and curvature while on the other side there are people like the famous computer scientist Dijkstra who insist that right from the start, students should learn rigorous abstract concepts. My own belief is that majority of people develop appreciation for mathematics only through specific examples and that it takes a level of expertise before which one may start appreciating rigorous mathematics. I belong to the first category of people who think that playing games, looking at bicycle tracks and thinking of real life situations is a much better way of getting introduction to mathematics.

Network Analysis with R

We are organizing a workshop “Network Analysis with R” at the Ahmedabad University, all interested are welcome. Here are the details.

Title : Network Analysis with R
Date: 29 February 2020

Venue: Ahmedabad University

Introduction
Ahmedabad University in collaboration with IEEE student branch of Ahmedabad University invites applications for a one day workshop entitled “Network Analysis with R”. The workshop aims at introducing the fundamental concepts of graph theory and methods of network analysis and visualisation. Network representation of data provides valuable information about the nature of interactions within the components of the system. Graph theory based analysis is now widely used to explain the information flow across the nodes constituting the network and also to hypothesize strategies for efficient channelling of resources across the network. Researchers in fields like biology, computer, management, and social sciences frequently employ techniques of network analysis and modeling.  Participant would have an opportunity of hands-on learning using R programming environment. 

Who should attend this workshop? 
The workshop would be of use to anyone who is interested in learning network analysis which can be applied to do research in various disciplines. Participation is open to faculty, post-docs, Phds, masters, and undergraduate students. Previous knowledge of programming is not an essential requirement to register for this workshop. 

To apply, please register at (google form link), By 21 February 2020.

Confirmation will be intimated by: 24 February 2020.

Confirmed participants will be required to pay the registration fees of Rs. 250/- on the day of workshop. Participants should bring their laptops.