[Mathematics] Sum of angles of triangle [Updated]
-
and "dark" matter/energy, i.e stuff we don't know or haven't imagined yet.
dark matter is just some more Higgs, painted black to fool us all. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
It is all relative. The surface of a sphere is a two-dimensional object: you can draw lines on it, delimiting an area, etc. You could always read more about it, however you would never see the end of it. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
d@nish wrote:
that cannot be drawn
Can you draw a straight line of length 1 meter? If you accept your pencil/pen/whatever has a certain width and you are satisfied that lengths and widths should not be more accurate than said width, then you can draw it perfectly. Same for circles, and hence also for SQRT(3) and many more irrational numbers. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
Luc Pattyn wrote:
surface of a sphere is a two-dimensional object
don't think that's true since it moves through length, width AND height.
in your Cartesian mind, yes. If you were the captain of a ship on one of earth's oceans, you would see longitude and latitude (hence two dimensions), and no third one, at least as long as you stay afloat. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
no, it just means you can't accurately measure the sqrt(3) side.
-
Luc Pattyn wrote:
Can you draw a straight line of length 1 meter?
Depends on the accuracy rate we agree upon. :)
OK, you choose the accuracy, we verify I can do 1 meter; next I will do SQRT(3) meter with the same accuracy, as outlined earlier. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
No. You not being able to do something does not prove or disprove something else. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
OK, you choose the accuracy, we verify I can do 1 meter; next I will do SQRT(3) meter with the same accuracy, as outlined earlier. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
Well since the square-root of 3 is a non-finite number, no you couldn't draw the line. Hence the figure drawn would not be a triangle at all since the two lines would never meet and the figure would not be closed. Ergo, the "point" were one side "doesn't meet" with the 3^1/2 side has no angle.
ahmed zahmed wrote:
the square-root of 3 is a non-finite number
It is finite. I think the word you are looking for is "irrational". Another irrational number is 3.14159...
-
in your Cartesian mind, yes. If you were the captain of a ship on one of earth's oceans, you would see longitude and latitude (hence two dimensions), and no third one, at least as long as you stay afloat. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
actually you do see a third one: the horizon is curved. (and not because there are waves)
-
ahmed zahmed wrote:
the square-root of 3 is a non-finite number
It is finite. I think the word you are looking for is "irrational". Another irrational number is 3.14159...
no, I said the correct word: non-finite (or infinite). The number of digits is not countable, ergo it is infinitely long and yes, not rational, i.e., not complete comprehensible.
-
I see it more like this: if X states Y is possible and I know Y is not possible, X has to be wrong.
well, I can draw a line of length 1 or of length SQRT(3) equally well as you can not prove I can't draw them. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
If we go for 100% accuracy, latter is not possible. If we go for anything less than that, latter wont be correct.
if you want 100% accuracy, then stick to math, and don't draw anything. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
if you want 100% accuracy, then stick to math, and don't draw anything. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
That's what I am saying with 100% accuracy, one cannot draw the 30,60,90 triangle. Never mind. I am off to sleep now. Good day. :)
Nor can you draw a 1 kilometer straight line with 1 micron accuracy. Good night to you. :)
Luc Pattyn [Forum Guidelines] [Why QA sucks] [My Articles]
Prolific encyclopedia fixture proof-reader browser patron addict?
We all depend on the beast below.
-
Surface of sphere "can be" considered 2-d if we are considering a part of its surface where sphere is of astronomical radius or we consider extremely small part of the surface. Otherwise I guess it has to be 3-d.
No. the surface of any 3d object is 2d. It's not a Euclidean plane, but that's not the definition of 2d; it just means you need 2 (no more, no less) variables to define any point on the surface; eg latitude and longitude.
3x12=36 2x12=24 1x12=12 0x12=18
-
no, it just means you can't accurately measure the sqrt(3) side.
You can accurately measure sqrt(3) side as well as you measure the 1 side. The difficult is to measure the sqrt(3) side by means of 1 side. :)
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler. -- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong. -- Iain Clarke
[My articles] -
no, I said the correct word: non-finite (or infinite). The number of digits is not countable, ergo it is infinitely long and yes, not rational, i.e., not complete comprehensible.
You're wrong: it is finite. The number of digits representing the number is an infinite one. According to your definition, even
1/3is an infinite number.If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler. -- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong. -- Iain Clarke
[My articles] -
We have learnt that sum of angles of a triangle is 180 degree. Now, 1, 3^1/2 and 2 form a triangle (based on the trigonometry). Since one cannot draw a line of length 3^1/2, this triangle is not possible which in turn means that sum of angles of a triangle is not 180 degree. Long ago, I had a read a book which stated that sum of angles of a triangle is not 180 degree (it was proven through a triangle formed by centers of three stars). I guess it was non Euclidean or something geometry. Anyone aware of this? And does anyone knows nice book where I can read more about that geometry? Edit: It is past midnight here. Time to sleep. Have a good time everyone.
Geometry simply doesn't care you can't draw exactly a sqrt(2) line (and you can't draw exactly a 1 line as well). :)
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler. -- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong. -- Iain Clarke
[My articles] -
actually you do see a third one: the horizon is curved. (and not because there are waves)
You cannot perceive that: you're a bidimensional captain. :)
If the Lord God Almighty had consulted me before embarking upon the Creation, I would have recommended something simpler. -- Alfonso the Wise, 13th Century King of Castile.
This is going on my arrogant assumptions. You may have a superb reason why I'm completely wrong. -- Iain Clarke
[My articles]