![]() Line, and the only point on the circle- the only point So you could have a lineĮxactly one point. Now you can also have otherįorms of lines and line segments that interact Line segment AB, and so is line segment- let meĭraw another point on here, let's say this is X- so line That we definitely know what we think we know. Interesting results and proving to ourselves It at the high school level, is it's probably theįirst class where you're introduced into a slightly moreįormal mathematics, where we're a little bit more carefulĪbout giving our definitions and then building And what's interestingĪbout geometry, at least when you start learning And you're probably alreadyįamiliar with the word radius, but I'm just being a Radius, AB over here, is equal to 2 centimeters. To a point on the circle, we would call a radius. ![]() Segment, I should say, that connects the center ![]() Is all of the points that are equal distance AB connects the center and itĬonnects a point on the circle itself. What I want to do is thinkĪbout what line segment AB is. Of these line segments that join A, which we wouldĬall the center of the circle. Some of the concepts and words that we use whenĭealing with circles. That are 3 centimeters from A, it might lookĭo in this video is introduce ourselves into But that is the formalĪre a fixed distance, or that have a fixedĭistance from A. And this set of allĬentimeters away from A, this is a circle, as I'm sure Line over there, which maybe I should just, let meĬlear out all of these and I'll just draw That it's only the points where there's white, it's all of Looking shape, like this, and I'm trying to Set of all of the points that are exactly 2Ĭentimeters away from A, I will get a very familiar So AC is also going to beĮqual to 2 centimeters, but I could go 2 centimeters ![]() In the other direction, maybe get to pointĬ right over here. But I'm not curious just aboutī, I want to think about all of the points, the setĬentimeters away from A. If I wanted to put units IĬould say 2 centimenters. I could say this looks nice,īut if I talk about its length, I would get rid ofĪB is equal to 2. I call that point, point B, then I could say line This point right over there, is 2 centimeters from A. Start at A and I go 2 centimeters in that direction, My screen right over here, that are exactly 2Ĭentimeters away from A. And what I'm curious about is all of the points on (For instance, the four corners of a square cannot lie on any legitimate parabola no matter which way the directrix is facing.) Hope that wasn't too far afield for you! With this more flexible notion of what a parabola is, now it would generally take FOUR points to define the parabola, and there are a couple of extra exceptions beyond the fact that no three of them can be on a straight line. If you're okay with the line not being horizontal, then you're going to get shapes that aren't the graph of a function, but a circle isn't the graph of a function either because lots of vertical lines cross it in more than one point. We talk about a parabola as being the locus of points that are the same distance from a given point and a given line, but nearly all the time we only consider the case when that line is horizontal. I don't want to get too weird, but parabolas are a little more complicated. Given any three points that aren't on the same line and with no two points on the same vertical line, there is exactly one quadratic function whose graph passes though those three points. The rules for quadratic functions are the same as the rules for circles.
0 Comments
Leave a Reply. |
Details
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |