From https://mathworld.wolfram.com/MetricSignature.html
"For n-dimensional Lorentzian space Rn-1,n , the metric signature is (n-1,n) , e.g., (3,1) (as above) for the Minkowski space of special relativity."
So if I understand correctly (wishing to be corrected), perhaps by "changing" the...
Thank you, vanhees71, for your interesting answer, including your answer (if I understood correctly) turning my suspicion of "necessary but not sufficient" on its head into "sufficient but not necessary". It appears to me (but I am willing to be corrected) that this contradicts the assertion in...
A couple of the sites that say that the vanishing commutator defines causality:
https://www.physics.umass.edu/events/2020-02-07-causal-uncertainty-quantum-gravity
https://phys.org/news/2019-11-aspects-causality-quantum-field-theory.html
Is "define" too strong?
Or, to put it another way: cannot...
Thanks for the suggestions, sophiecentaur. I shall try them. Hopefully she will be able to compare the drawing with what she has on her roof, since she can't actually get too close to it.
By the way, where is your signature saying "If God had intended us to use analogies, he would not have...
Thanks for the information, cmb and sophiecentaur. The original purpose of wanting to know f/D was to be able to draw a simplified cross-sectional parabola with an 11-year old, which, given that I had "D", could give me "f", which would allow the pupil to figure out the equation of a parabola...
Actually, very little sanding is necessary. 😁Try distinguishing (by eye; furniture buyers don't come with their calculators ready) the conjunction of the four arcs;
centre (1.5, 0), radius 2.5, for x between 3 and 4
centre(-1.5, 0), radius 2.5, for x between -4 and -3
centre (0, 2), radius 5...
Super! :woot:The link looks like it contains lots of useful stuff, thanks.
The two-pin-and-a-string method is of course classic for an ellipse; wandering around the Internet a while back I was amused to find that carpenters (or at least the traditional type, not the ones that mass-produce and...
Thanks, Tom and sophiecentaur
Tom: You are right, the second link is more useful with some very nice simple diagrams that can be used to give the general idea of an offset antenna to a school pupil without going into the mathematics (which is as much as I will cover with this pupil). I will...
Suppose we started with a simple case, where the paraboloid was not offset but was a rotated parabola; then from the D Diameter (20 inches) and the f/D, one has the focal length, and the student could write the equation of the generating parabola.
Thanks. Also thanks that you have removed them from the visible post. (Interestingly enough, they reappear when I press "edit".)
Indeed, I am starting quantitatively on finding the focal distance of a simple parabola, and then only qualitatively discussing the idea of cross-sections of a dish...
Thanks, Baluncore, sophiecentaur, hutchphd, dlgoff, and berkeman. Some comments:
Indeed, I had a friend in the US contact the company involved and ask for the depth, focal distance, and/or f/D ratio, and when, in response to the chat request for a 16-digit number on the bill, my friend...
Just to see if I understand this, I refer to a generic picture (this is not the antenna concerned, but a photo with no brand names on it, so as not to trespass any legal boundaries with which I am not familiar): are you saying that the focal distance is the length of the bottom bar in this picture?