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Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.So that ifθ = arcsin v/candα = cos θβ = sec θthen length contraction l and time dilation t can be expressed asl = Lαt = Tβwhere L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.

Quote from: jeffreyH on 04/09/2016 14:40:29Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.So that ifθ = arcsin v/candα = cos θβ = sec θthen length contraction l and time dilation t can be expressed asl = Lαt = Tβwhere L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.It is interesting how ''alien'' something looks when a person like myself does not understand it. Can you first explain cos and sin in simple terms?

Quote from: Thebox on 05/09/2016 10:15:20Quote from: jeffreyH on 04/09/2016 14:40:29Inspired by David Cooper I have put together the following. The range 0 to 1 relates directly to the sine and cosine functions within the range 0 to π/2 radians. This range can be used to represent the ration v/c that shows up as the ratio of squares in the gamma function.So that ifθ = arcsin v/candα = cos θβ = sec θthen length contraction l and time dilation t can be expressed asl = Lαt = Tβwhere L = proper length and T = proper time. If we set c = 1 then we can relate this to the unit circle. This applies to quadrant I where all values are positive. Investigation of the angles involved and what they might imply is ongoing.It is interesting how ''alien'' something looks when a person like myself does not understand it. Can you first explain cos and sin in simple terms?https://en.m.wikipedia.org/wiki/Trigonometric_functions [Links inactive - To make links active and clickable, login or click here to register]

Careful now people might actually get the impression that you know this stuff. That can't possibly be true.

I don't know this although I have glanced cos and sin before. I have no idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ?

Quote from: Thebox on 07/09/2016 08:49:42I don't know this although I have glanced cos and sin before. I have no idea why we call it cos and sin when x and y would seem to do, why do we rename X and Y ? You are not just renaming them. You are using them in a formula, so you can show how x or y varies with the value of different angles, the protractor won't do that.Have a real look at the link Jeff gave, not just a glance. This is one of the fundamentals of maths and it's worth understanding.Note I say understanding, not just learning by rote.PS you can find some good maths textbooks in German if that helps []

Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).

QuoteThink of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians).Oh no they won't!

P.S. There are 3 angles.

Quote from: jeffreyH on 08/09/2016 00:58:24P.S. There are 3 angles.Now I am confused you seem to be arguing with each other about a triangle. A triangle has 3 ''sides'' If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?

Quote from: Thebox on 08/09/2016 08:14:02Quote from: jeffreyH on 08/09/2016 00:58:24P.S. There are 3 angles.Now I am confused you seem to be arguing with each other about a triangle. A triangle has 3 ''sides'' If cos=sin we have one 90 degree and two acute angles, if a triangle is an equilateral triangle, there is no 90 degree and 3 acutes?Sorry for confusing you. Yes there are 3 acute angles in an equilateral. Keep on going. It's worth the effort.

The only time cos x = sin x is when x = pi/4 or 5pi/4.Wake up, guys, this stuff is pre-'O' level - in fact only just post-11-plus!

I strongly advise you to learn some elementary maths before paddling in the waters of science. Maths is the language of physics just as German is the language of Germany.

If cos is ten miles long and sin is ten miles long, then surely cos=sin? or am I confusing this with calculus?

Quote from: Thebox on 08/09/2016 10:15:57If cos is ten miles long and sin is ten miles long, then surely cos=sin? or am I confusing this with calculus?Cos, sin and tan are not distances but ratios. Start with basics https://www.mathsisfun.com/algebra/trigonometry.html [Links inactive - To make links active and clickable, login or click here to register] or you will always be confused.

. and tangent is always an ''hippopotamus''? lol.

Quote from: Colin2B on 08/09/2016 23:37:12Quote from: Thebox on 08/09/2016 10:15:57If cos is ten miles long and sin is ten miles long, then surely cos=sin? or am I confusing this with calculus?Cos, sin and tan are not distances but ratios. Start with basics https://www.mathsisfun.com/algebra/trigonometry.html [Links inactive - To make links active and clickable, login or click here to register] or you will always be confused.Thank you Colin, that link looks a bit easier to understand. I have the link open has I write. Sine Function:sin(θ) = Opposite / HypotenuseCosine Function:cos(θ) = Adjacent / HypotenuseTangent Function:tan(θ) = Opposite / Adjacentcos is always the adjacent?sin is always the opposite?and tangent is always an ''hippopotamus''? lol.

Ok, back to the point. The past and future light cones are related to Minkowski spacetime as can be seen on the following page.https://en.m.wikipedia.org/wiki/Light_cone [Links inactive - To make links active and clickable, login or click here to register]I will be relating trigonometry to both Minkowski spacetime and the light cones in a slightly different way.

I don't mind as long as you stay on topic. And don't ask about equilateral triangle's. Lol.

Hi Box,What's the problem with light cones? They're simply a way of showing a sphere expanding over time by eliminating one (or two) space dimension(s) from the diagram and using one of the freed-up dimensions (the one running up and down the page) to show time. The cones that you're rejecting are pictures of a sphere expanding, so you just have to learn to read them the right way to recognise that.

The light cone is a valid mathematical construct.

The interpretation of future and past is incorrect and a cone is not a sphere, the diagram looks like an over exaggerated Pulsar.

And now here's a similar set of diagrams which attempts to do the same thing with another space dimension included, so it's an expanding circle shown at higher levels in the cone each time. The top left diagram shows four photons moving outwards from the centre, but it's a confusing mess, made worse this time by the lack of numbers to help you work out which photons are the same photon at different times as they move apart. The diagram under it shows the same thing, but looking in at an angle such that the photons moving up and down the screen appear to be moving more slowly, but you should be able to imagine that they are on a surface like a table set out in front of you and that all four photons are still moving apart at the same speed as each other. The diagram on the right shows the same action again, but this time it uses height up the screen to indicate time, but with a complication in that after the photons have moved away from the start, the nearest photon to you is then shown lower on the screen than the one furthest from you for the same moment in time - this is the result of the limitations of trying to show three dimensions (two of space and one of time) on a 2D screen. I won't even attempt to show all three space dimensions plus one time dimension on a 2D screen - you are expected to use your imagination to make that leap for yourself, but the idea of using cones to describe expanding spheres is fully valid.

Scratches head trying to relate any relativity to your diagrams.

Quote from: Thebox on 12/09/2016 19:48:40Scratches head trying to relate any relativity to your diagrams.Perhaps you need to find an expert where you live to discuss this kind of stuff with so that they can do it more effectively than is possible through texts and static diagrams. It will likely take a lot of demonstrations in the air with lots of hand waving to get the ideas through.

Think of a triangle with all 3 sides the same length. Two of the sides will form a right angle of 90 degrees (pi/2 radians). Sine, cosine and tangent can be described by the 'word' sohcahtoa. This stands for sine is opposite side divided by adjacent side, cosine is adjacent side divided by the hypotenuse and tangent is the opposite side divided by the adjacent side. Let me know when you have worked out why this is true. And no nonsense.