When I was a teenager one of my friends at the time was convinced the fastest way around a racetrack was to hug the inside of the corner. No amount of me trying to explain the correct strategy of starting wide, turning in, cutting the apex and accelerating out of the corner ending up wide again could convince him otherwise. Even watching an actual race or playing a simulation racing game and trying it himself could not convince him he was wrong.

I'm guessing in this case there would never be any hope to convince this particular person but that recently got me wondering... Is there a way to show using maths what the correct method of cornering is?

I'm thinking maybe it would be something to do with deceleration and acceleration vs distance but the fact is while I'm a great racer in games I couldn't do a complex maths problem if my life depended on it.

So is there anyone here that knows a little about maths and racing that could give me some ideas of how this explanation would go?