Rolled up Yoga Mat(h)

This is really an elementary problem in geometry and algebra. It is not puzzling nor are there any twists. The result is interesting.

I came across this intriguing problem a couple of days back. On my return from my recent trip to USA I found that my brother in law from US, who was on a reverse visit to India, had left behind one of those Yoga Mats of compressed foam. I normally use a simple folded blanket. The mat was kept tightly rolled in its card board carton. Presumably this is done to reduce the carton size.

I had to go through some non yoga contortions to straighten out the mat prior to use. Because it was tightly rolled it tended to curl up doing yoga of its own.

While doing yoga I got to considering what is the relationship between the ID (that is, the starting diameter) of the rolled mat and its final OD.

The mat is 200 cms long and 0.5 cm thick. Given this data it is fairly elementary algebra and geometry to work out the analytical relationship between these parameters.
Finally it ended up as a two column excel file. The first column is the starting dia of the roll (the central hole as it were) and the second is the (calculated) outer dia of the roll.

The results were quite unexpected and revealing.

Those curious can have a shot at this.


  • Ramani Aswath
    Ramani Aswath
    Raison de etre for the exercise:
    How much effect will making the roll have a larger central opening, which makes it easier to unroll, have on the OD of the roll and hence the carton cost?
  • Ramani Aswath
    Ramani Aswath
    One can use calculus, numerical methods or even more complex ways. I just assumed that the rolled up mat was a hollow cylinder with ID as the variable. The cross sectional area of this should be the area of the mat's edge. In this case 200 x 0.5 = 100
    Pi x (D^2 - d^2)/4 = 100
    D = Sqrt((400/Pi) - d^2)
    Solving this for various values of d is a no brainer.

    I found that for d varying from 0 to 5 cm the OD of the roll does not change by more than 1 cm.

You are reading an archived discussion.

Related Posts

UK's TWI has unveiled a 5 kW handheld laser gun that can cut through tough metal pipes like a hot knife cuts butter. All thanks to the fibre laser projector...
friends,do anyone know about water swirl algorithm?very urgent!
when will the rotor angle change in large alternators???
No doubt jQuery is most popular framework for Java Scripting on web. But novice developers feel it very complex. So here is Angular js to simplify dynamic java script framework...
Then GSM TDMA system uses a 270.833 kbps data rate to support eight user per frame, 1) What is the rate data provided for each user? 2) if guard time,...