What is Pascal's theorem?? I have no idea!!!
I need help
I have tried a lot of websites but i dont understand what they are saying. can someone dumb it down for me a little so i can understand it????
if we have a hexagon inscribed in a circle or conic section, and we extend opposite sides so that they intersect each other, we will get thre points of intersections all of which lie on the same line.
(the sites i gave you have many diagrams, so you can look at them to see what it's talking about.)
what does that mean?
a hexagon is a 6-sided polygon. drawing a hexagon inscribed in a circle means that we draw the hexagon within the circle in such a way, that all the vertices (or pointed edges) touch the outline of circle. conic sections are usually ellipses, these you can think of as elongated circles. so the idea is, whenever we draw a 6-sided figure within a circle or an ellipse, we can extend opposite sides so that the lines intersect. since we have 6 sides, there are three pairs of sides that we can extend. when we extend all these lines, we would have two of the lines meeting at one point, another two meeting at another point, and another pair meeting at another point. so we get three points. basically, Pascal's theorem says, we will always be able to draw one straight line that connects all those points, no matter the shape of the hexagon or the ellipse we inscribe it in.
now i guess we draw a hexagon in such a way, that the points of intersection are meaningful somehow, but i can't really help you with that part
try reading the websites again, very slowly. if they mention a word you don't understand, look that up separately and then go back and reread it. one of the sites i gave has an interactive figure. you can actually change the shape of the hexagon and it will move the line connecting the points accordingly, play around with this to see what's happening. once you fully understand the concept, think of how it relates to what you are doing in class, or what you did in class a while back. also think of ways the line could be useful, for example if we could get it to be a tangent to the circle, what would that mean? (a tangent is a line that touches the circle at only one point)
i'm off to bed, it's almost 4am now!