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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
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?