One of the actions is to find the points of intersection of a straight line with a circle. Here is a gif showing the result:
The algebra needed to solve the two simultaneous equations is straightforward, but a pain in the butt to get right and code up, so I thought “Why not solve the equations for the very simple case of the circle centered at the origin and the line vertical, at the same distance (a) from the centre of the circle
Then it is a simple matter of rotating the two points (a,b) and (a,-b) about the origin, through the angle made by the original line to the vertical, and then translating the circle back to its original position, the translated points are then the desired points of intersection.
The same routine can be used for the intersection of two circles, with a little bit of prior calculation.
Filed under geometry, math
Instructions: Read at least twice !
CCSSM talks about “the standard algorithm” but doesn’t define it – Oh, how naughty, done on purpose I suspect, since there are varieties even of the “American Standard Algorithm”. Besides, if it is not defined it cannot be tested (one hopes!). I checked some internet teaching stuff on it, and as presented it won’t work on for example 403 – 227 without modification.
Anyway, I was thinking about subtraction the other day (really, have you nothing better to think about?), and concluded that subtraction is easiest if the first number ends in all 9’s or the second number ends in all 0’s. So, fix it then, I thought, change the problem, and here are the results
I am quite sure that some of you can extract the general rule in each case, and see that it works the same in all positions.
While I am going on about this I would like an answer to the following-
“If I understand subtraction, and can explain the ideas to another, and I learn the standard algorithm and how to apply it, and I have faith in it based on experience, WHY THE HELL DO I HAVE TO BE ABLE TO EXPLAIN IT?”
I guess this post counts as a rant!