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

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?
Friendly greetings
Hero
PS. Maths is also about ,,spaces", which are sets with a structure.
And Cantor defined ,,Eine Menge ist eine Zusammenfassung bestimmter,
wohlunterschiedlicher Dinge unserer Anschauung oder unseres Denkens,
welche Elemente der Menge genannt werden, zu einem Ganzen. ,, A set is
a collection of specified, proper differentiated things of our
reception or reasoning (thinking), which are called elements of the
set, into a whole. (my translation). So in math we can talk about sets
of numbers as well as sets of dogs, sets of temperature changes,...

.

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