Going strictly from the rulebook you can not move in a curved line. All model advances are in a straight line exactly forward, granted you are allowed to stop and turn as many times as you like but what you are proposing is an infinite number of miniscule moves and turns. So using radial geometry to justify moving your models is not strictly correct from a black and white rules perspective.
To me that is a side issue however the more important part is you need to measure, and your opponent needs to see you measure ALL model movements. This is a sportsmanship issue. Simply saying "I have enough movement to get around this base because math" doesn't cut it, you need to measure the movement on the table at the time. Physically the base of the model needs to move through the space on the table that it is advancing through and you need to measure that with a suitable measuring device. Similarly it doesn't matter if a player is able to accurately measure distance on the table by eye they still need to measure it out, doesn't matter if they are right.
Yeah I'm with Ross on this one. My geometry from high school isn't great and that isn't the sort of maths I would be comfortable doing in my head. If we were regular players together and it had come up and you sat down with me and showed me until the point I was happy with that and then next time you were like "remember the math" that is 3 inches (for example) I'm pretty sure I would be cool.
Certainly if we were playing timed turns I wouldn't be happy with that either, too much going on to confuse my troglodyte intellect with what appears to be basic high school math.