How do calculators do this? From what I understand, a computer/calculator can only add or subtract, and nothing else. How exactly does it graph polynomials, calculate pi to hundreds of digits, etc.

 

I know how it does some of the things: e.g. it sums a series when calculating the cos(1), but what does it do when its calculating anything complicated like logarithms?

Well, graphing calculators have functions built into them that you just fill in. Also, it has a y= section (I have that kind: TI-82) that you plug, well, y= equations. I haven't figured out how to graph binomials or higher, but you can solve them as well in the matrix function. It's pretty cool. And I'm not sure about logarithms...

alot of time figuring out how to do various mathematical operations in a computer. there are now hardware functions for addition and division, and there are algorithms for graphing.

 

the graphing algorithm works the same way that a human works as they graph, plot a number of points, and then a draw lines to connect the points. By plotting enough points te straight lines begin to look curved.

from what I understand, it's all done with algorithims of approximations and summations.