Points, lines, segments, rays and angles are the building blocks of geometry. Understanding these concepts is essential, since they will be used in a wide variety of applications.
Points and lines are basic ideas (also known as abstractions) in geometry that do not have definitions - they are undefined terms. Points and lines are not things; they can not be seen or touched. However, our understanding of these ideas evolves out of our experiences with physical objects and situations that can be seen, touched or manipulated. For example, the notion of a point can be suggested by the tip of a pencil or the smallest dot you can make; it has no dimension. The notion of a line can be suggested by railroad tracks, a string held tight, or the path of a light eam. These physical models help cultivate the notion of these ideas in our minds.
Ancient Greek mathematician Euclid described a line by using two critieria or postualtes:
(1) through any two points there is always a line, and (2) every line contains at least two points. These postulates, which detail facts that Euclid believed were self-evident appear in every geometry book that has since been ever written.
We can verify the first postulate by drawing a pair of points. No matter how we draw the two points, a line can always be drawn through them. The second postulate uses the phrase at least two to describe the number of points on a line. Euclid knew that a line contains an infinite number of points. Why not simply state that in the postulate? One reason is that these postulates present facts that are the foundation for further geometry facts. Euclid wanted his postulates to be as simple and as brief as possible. At least two points allows for but does not stipulate an infinite number of points.
A segment is a part of a line that contains two points (called endpoints) and all the points between them. A ray is a subset of a line that contains a point (called the endpoint) and all the points of the line on one side of the point.
Think about what you have just read. Think about Eucalid's postulates. Think about how it changes or deepens (or confuses) your understanding of points and lines. Do you need to study more to get it? See what else you can find out to deepen your understanding.
Leave a comment on your thinking.
I would like to know more about Euclid. I did a projet on him last year, but I didn't get a lot of time to learn about his life. All I know is that he was a Greek mathematician. I also want to review the differences between lines, line segments, and rays. the differences confuse me a bit.
ReplyDeletePosted by: Black Arabian
The meaning to me is very confusing but it creared up some falts in my thinking. Also the Segment is very Very clear
ReplyDeleteIt makes perfect sense. It's hard to explain my thinking without drawing an example,since I'm such a visual person.
ReplyDeletethis was very confusing at first, but if u read the sentecnes over then it makes perfecct sence. I would like to learn more about Eucalid
ReplyDeleteThey can't be seen or touched? What are postulate's. O great more math words ."I'm so confused". so a line has a infinite number of points. cool!
ReplyDeleteI don't really understand this too much but I get this... line segments have two end points, a ray has one end point and goes on in enfinety in the opposite diretion and lines go on for enfinety in both directions.
ReplyDeleteI dont understand much of that and I want to know about postulates and euclid.
ReplyDeleteAll these fancy words and paragraphs are getting me confused!I think I need more study to fully understand. It also deepens how I think about geometry. I can't believe how many people study so much about geometry like Euclid.
ReplyDeleteI got this bang-on, but I would like to know about more mathmatichans and their postulates. (And maybe prove them wrong, if they are!)
ReplyDeleteBy: The Blizzard Dumpster
I think I would need to reseach more on Euclid, and his postulates,this article really stumped me. It got me thinking like why he wanted his postulates to be as simple as possible. But over all it was very convusing to me and I had a hard time understanding everything , like what is a postulate?I should go find out!
ReplyDeleteThis is a lot to think about. All of it is true though. For example: It is right , to say that points, lines, segments, rays, and angles are the building blocks of geometry. Without them we could not measure angles. Euclid is very smart, I would definatly like to learn more about him, and his studies. I think to actually understand some of the desriptions, I need to study more. I did look up a description of rays. A ray is a line that starts at one point (called an endpoint) and goes on forever in the other direction. Does that help?
ReplyDeleteEucalid's thiking really deepens my understanding of lines and points. It is really cool how lines no matter how you position the pionts there is alway a line segment that you can position between them.
ReplyDeleteI don't think that every line contains at least two points. Since a line is infenent it has no point in which it ends so it doesn't have two points on each end. It doesn't have to have two points, but it can.
It is so awesome the way the old Greek math theories are still used today. I can't belive they survived all those years.
Coolcab
first of all that was very confusing but after I reread it a few times I absorbed the text and I would like to tell you what I learned and what no matter how many times I read it will not make sense. I learned what postulates means and all of the paragraphes helped me understand better some of the concepts that I had not thought much about. I do not know what subset means. I learned alot from this thing-a-majig.
ReplyDeletesincerely,
A Pirate
I am so confused!!! I really need to study more!!! I aggrie with Euclid's theory about the discribtion of the line and point. "through every two points there is a line" and "every line contains two points"!
ReplyDeleteThey also conects to each other.
I thoght I needed more info about postulates so I looked online this is what I found . . . . . .
ReplyDeleteI found lots of definision's each very different, I was ready to give up but then I saw a definion that said mathamatics above it ..."a statement that is assumed to be true but has not been proven and that is taken as the basis for a theory, line of reasoning, or hypothesis"it definiatly helped me understand more.
A postulate is a true statement, which does not need to be proved. For example, the sum of the interior angles of a triangle add up to 180 degrees. We know this and it does not need to be proved. Another example is if there are 2 lines on a page, they can only cross each other in one spot. Yet another example is a circle has 360 degrees. We know all this; it does not need to be proven.
ReplyDelete