Curved to Rectangular Distribution

[X_Art_X]

Hi Guys :)
I have become interested in producing true random numbers of uniform distribution,
and have come across this Numberphile video in my travels:


The narration hints at the topic of converting numeric sequences of a curved distribution,
inherently more likely to be closer to a mean peak, than the outer edges of the curve,
to a rectangular (uniform) distribution of random numbers
(which occurs to me more useful if you were selecting lottery numbers or something like that.
The narrator avoids the topic of the math to do the job, presumably too difficult or too boring for the video.

Would anyone lead me to something to study on that topic?
Considering I’m a hobbyist with senior high school level education, the simpler the better.
I presume this is an intermediate question as I am still familiar with high school math.
Thanks, Art.

 

[RUber]

I would recommend picking up a book on modeling and simulation. These books normally cover the different transformations between distributions so that you can simulate a variety of distributions from uniform random number generators.