Triangle Inequality

Experiment

• Clear out a small area. Mark two points at the far ends of the area as ‘start’ and ‘end’. Ask some students to run across from ‘start’ to ‘end’. What kind of path would they pick? The straight-line path between the two points? Now ask them to walk from start to end via some other point not on the straight-line path. Why do they show resistance to that method?

• We always like to walk across lawns to get from one side to another, than go all the way around. Why?

Fastest way to reach END from START

Walking along the black line is faster than the other paths from START to END

We intuitively know that the shortest path between 2 points is a straight line

If you were to not follow a straight line, the alternate path forms a Triangle

START

END

This is true for any triangle

• The third side of a triangle is always less than the sum of the other two sides

START

END

This is called the TRIANGLE INEQUALITY

Applications

• Airplanes fly through the shortest path

• Direct trains faster than connecting trains• Why do farmers put barriers around their

farms? So that people don’t take the shortest path that goes through the middle of the farm

How to design a good experiment

• Closer Feedback Loops. Knowledge Gratification.

• How can I do something better that I already do by having knowledge.

• Big ideas ? But can we try ?