Mathematics in Crime

Mathematics in crime 

Have you ever heard about hit and run case that remained unsolved for a year or longer? That may be because of the fact detective did not use mathematics to solve the case. Wait! What? Mathematics to solve a crime? Yes, mathematics could help a lot in this scenario. Let me elaborate you.

Imagine a person hit by a bike and the bike ran away and you are given this hit and run case to be solved. But the only clue you have is the track of the bike on the road spot. What will you do? First, you should think about which direction was the bike coming from during the accident? Suppose these are the tracks of the bike.   

 Can you find the direction of the bike?

Can you tell the size of the bike?

Yes we can find both.

But the problem you may face is you encounter two tracks overlapped with each other. To know the direction of the bike first you have to find which of the two sets of the tire is the back tire? So here you should use mathematics.

1.   If you look at the track the front tire is always pointing in the direction of the bike but the back tire is pointing towards the front tire. If you draw a tangent on any back tire it will always intersect at some point on the front tire.

  

So if you get any point on any track where tangent at that point is not intersecting the other track, then it is the track of the front tire.

2.   Here the dotted path is the front tire.

 

But we have not found where the bike came from? To find that we should think much deeper. We should know that the tangent from the point on the back tire must always intersect the front tire track and the length of the tangent always must be equal to the size of bike.

 

3.   Suppose we found that the tangent at our back tire track always intersect front track and gives the length of the tangent always constant only if tangent is drawn right. But while producing tangent towards left it is intersecting the front tire with the variable length which is not equal to the size of the bike.

4.   And in the process, we already found the size of the bike.

-SACHIN SAUD