Re: Geometry: No four vectors can be pairwise at an right angle to each other


Hero wrote:
Randy wrote:
...vectors which are orthogonal under the the
dot product form right angles in the sense in which
Euclid defined them.
Randy wrote:
There is no such thing as vectors which are orthogonal
in that sense which do NOT form right angles. Is that
clear enough?
Randy wrote:
[snip random word salad].
You wrote a bunch of random gobbledegook and did not comment
on the above.
Do you agree or disagree: There is no such thing as vectors
in R^n which are orthogonal under the dot product and which
do not form right angles.
I tried my best in giving You an answer.
You seem to have an interpretation of ,,right angle", which is
different from mine.
There are many R^2: a pure number space, a geometric one or... or
consider the change of temperature with time at a certain locality.
This last one is often displayed graphically. Here one has vectors too:
a rise of three degrees in four hours = ( 4 h, 3 d ), this one is in
one graphics at an right angle to a fall of three degrees in the
following 2 hours and 15 minutes = ( 2.25 h, - 3 d). Do You claim, that
there is an right angle between a certain rise in temperature and a
certain fall of temperature?

No. I claim that the GRAPHS of these two lines, which are
geometrical constructs formed of geometrical objects (lines in
a plane) form a right angle, a 90 degree angle in a plane, in
exactly the Euclidean sense.

- Randy

.

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