Recent content by Trysse

About two years ago I had a thread here, where I was looking for a way to calculate the distance between two points A and B on a plane when the following information is given: The distances of the points A and B to three arbitrary (but non-colinear) reference points. The distances between the...

Although I have enjoyed the discussion, I find, that it is beside the point (of the OP). The Idea of the OP was to present the scenario without any narrative tweaks and turns that make the description paradoxical. The paradox arises in the way the story is told. If I tell the story as "the...

This is a response to a recent insight article regarding the twin paradox. The idea is to model the most basic scenario in a way, that the paradox disappears. This basic scenario and its kinematic effects are then modeled using only a straightedge and a compass. The best way to read this post...

I don't know if it is trivial, because I am hopeless when it comes to proofs. However, I am not so sure if it is obvious. Many geometric relations are obvious once you know them. So maybe I should rephrase my question: "Is it common knowledge?" What do I mean by this: If I ask random people...

Given a cartesian coordinate system with a fixed point of origin and three axes, it is a fact, that the coordinates of a point P change, when the coordinate system is rotated around its point of origin. The distance between the origin and point P is of course unaffected by such a rotation. What...

Thanks, that was helpful. Good point. I knew that "squaring the circle" was impossible, but I did not make the connection. I knew the term transcendency but was unaware that this had a geometric consequence.

Is there any way to construct a line segment, that has the lenght of the circumference of a circle using only a ruler and a compass? My intuition says "no" Or phrasing the question in another way: given two line segments, can I prove, that the longer line segment has the length of the...

Just heard this Podcast about the Gold Standard. Found it very interesting and it gives a quite differentiated but still compact discussion about the topic. https://www.bbc.co.uk/programmes/m0013hh7

I am looking for more books like this one: https://archive.org/details/MethodOfCoordinateslittleMathematicsLibrary Method of Coordinaes (Little Mathematics Library) by A. S. Smogorzhevsky I am also interested in papers if you can suggest any. I am interested in texts, that explore the idea of...

There is a book by Joe Haldeman, The Accidental Time Machine, which somehow takes the spatial movement into account. However, in the book this does not take the time traveller into space. Just somewhere else on earth.

I usually think of a sphere as the set of all points ##P_x##, that have the identical distance r to some point ##C## which is the center of the sphere. I calculate the surface area ##A## of the sphere as $$A=4 \pi (C P_x)^2$$ However, what happens if I think of the distance between the points C...

@andrewkirk thanks. That is what I was looking for.. I would have never found this theorem on Google. I was always searching for "geometric mean, & circle & proof" but never for "chords".... Thanks for pointing me in the right direction.

Given are a fixed point ##P## and a fixed circle ##c## with the radius ##r##. Point ##P## can be anywhere inside or outside the circle. I now draw two arbitrary lines ##l_1## and ##l_2## through the point ##P## in such a way, that both lines intersect with the circle ##c## in two distinct...

It wasn't meant as claim. But I take the point: It was a sloppy formulation that had an (implicit and) unjustified reference to a source. So, could I say/write: In physics, events are often referenced by a four-dimensional tuple (t,x,y,z). The first coordinate describes when an event takes...

This is a historical question regarding SR. Has any physicist before EInstein multiplied the time coordinate with the speed of light? If yes who was it? What is a good book or paper that discusses why and how Einstein (or others before him) have come up with the idea to multiply c and t? When...