3 (at least) definitions of 'angle' ?!?!

paulb203 · 2023-12-16 03:02:26

I like the definition for 'angle' given here on Maths is Fun;

"The angle is the amount of turn between each arm," next to the illustration of said arms, joined at the vertex.

Another site defines the angle as THE SPACE between two intersecting lines.

Q. Do the lines (arms) in the MIFun illustration intersect? Or merely meet/join, at the vertex?

Another defines the angle as THE FIGURE FORMED when two rays share a common endpoint.

Q. Regards the two former definitions (amount of turn/space between); am I correct in thinking these don't include the arms and the vertex as part of the angle itself, the angle in the first defintion being how much the arms move, the angle in the second being how much space is created between the arms after they've moved?

Q. Regards the latter definition (the figure formed...); does this include the arms and the vertex and the space created/amount of turn, i.e, the whole thing?

Last Q. When a straight angle is shown in an illustration, i.e, basically a straight line, usually (always) with a semi circle added, and a dot in the middle of the line, should we see this as two arms opened up 'flat' with the dot as the vertex?

KerimF · 2023-12-16 04:00:52

Your remark is interesting.

As you know, a line is formed by dots (geometrical dots).
And by definition, a geometrical dot has no dimensions; actually, this means that it could be given any dimensions.

To answer your questions (confusion), we can assume that the dimensions of the dots forming the arms and the vertex of an angle are infinitesimal small (close to zero, though they are not in our drawings using a pen). This makes all definitions, you presented, be equivalent to each other, at least in theory (speaking geometry).

amnkb · 2023-12-17 08:34:46

paulb203 wrote:

Q. Do the lines (arms) in the MIFun illustration intersect? Or merely meet/join, at the vertex?

"intersect" doesn't have to mean "cross and continue"
It can mean "meet" or "just touch" like a repeated root of a quadratic just touches the x-axis

paulb203 · 2023-12-19 23:49:26

KerimF wrote:

Your remark is interesting.
As you know, a line is formed by dots (geometrical dots).
And by definition, a geometrical dot has no dimensions; actually, this means that it could be given any dimensions.

By 'geometrical dot' do you you mean a point? As in the point given by cartesian coordinates?

And why could it be given any dimensions?

paulb203 · 2023-12-20 00:17:20

amnkb wrote:

paulb203 wrote:
Q. Do the lines (arms) in the MIFun illustration intersect? Or merely meet/join, at the vertex?
"intersect" doesn't have to mean "cross and continue"
It can mean "meet" or "just touch" like a repeated root of a quadratic just touches the x-axis

Ah, that's interesting. The Math is Fun dictionary gives the following defintition for intersect.

"To cross over (have some common point)"

The first part (to cross over) seems to imply cross and continue, yeah?
Whereas the second part (have some common point) suggests that to "meet" or "just touch" would satisfy the criteria, yeah?

paulb203 · 2023-12-20 00:42:52

I just noticed that in some questions for finding an angle instead of asking,

"Find angle x" the question is instead, "Find m angle x," m standing for measure of angle x.

This is interesting.

Q. Is it incorrect to say, for example, "Angle x is 45 degrees"?

Q. Would it be more correct to say, "The measure of angle x is 45 degrees"?

Again, we're back to how we define 'angle' (measure of turn/amount of space between/ figure created...)

Tricky one...

KerimF · 2023-12-20 02:12:14

For instance, when I was a student in schools then universities, I used to (actually I had to) follow, in every exam, the definitions that pleased the teacher in charge of it.
After graduation, I was able to start a private business as a designer in electronics for the local consumers (I am 74). And since then, I used to follow at work what pleases me only

amnkb · 2023-12-20 02:22:53

paulb203 wrote:

...defintition for intersect: "To cross over (have some common point)"
The first part (to cross over) seems to imply cross and continue, yeah?
Whereas the second part (have some common point) suggests that to "meet" or "just touch" would satisfy the criteria, yeah?

Agree

paulb203 wrote:

Q. Is it incorrect to say, for example, "Angle x is 45 degrees"?

Technically, yes, I think
but everybody uses this lingo & everybody understands what yu mean

paulb203 wrote:

Q. Would it be more correct to say, "The measure of angle x is 45 degrees"?

agree

Last edited by amnkb (2023-12-20 02:23:14)

Math Is Fun Forum

#1 2023-12-16 03:02:26

3 (at least) definitions of 'angle' ?!?!

#2 2023-12-16 04:00:52

Re: 3 (at least) definitions of 'angle' ?!?!

#3 2023-12-17 08:34:46

Re: 3 (at least) definitions of 'angle' ?!?!

#4 2023-12-19 23:49:26

Re: 3 (at least) definitions of 'angle' ?!?!

#5 2023-12-20 00:17:20

Re: 3 (at least) definitions of 'angle' ?!?!

#6 2023-12-20 00:42:52

Re: 3 (at least) definitions of 'angle' ?!?!

#7 2023-12-20 02:12:14

Re: 3 (at least) definitions of 'angle' ?!?!

#8 2023-12-20 02:22:53

Re: 3 (at least) definitions of 'angle' ?!?!

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