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- Jan 17, 2014
Help! Mathman!
- Thread starter CoyoteChris
- Start date
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- Dec 4, 2004
I verified - you are correct!
If a spaceship is going 2/3 the speed of light and is flying by the earth, then turns its headlights on to illuminate the bucket in my back yard, how fast is the light going in the frame of reference of the space ship, and the earth?
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The speed of light..
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- Jan 17, 2014
The power of induction.
Theorem: all cats are orange.
Proof by induction.
Start with one cat. His name is Felix and he is orange. So we proved it for 1.
Now the induction step: assuming the theorem is true for n cats we will prove it for n+1.
So we have n cats, which are, as we proved, all orange. Now let's add a new cat to the collection. We must prove he is also orange. So take away one cat from the existing collection of n cats and replace it with the new cat. But we already proved that any n cats are all orange, so because the new cat is in the collection he must also be orange.
The theorem is true!
Theorem: all cats are orange.
Proof by induction.
Start with one cat. His name is Felix and he is orange. So we proved it for 1.
Now the induction step: assuming the theorem is true for n cats we will prove it for n+1.
So we have n cats, which are, as we proved, all orange. Now let's add a new cat to the collection. We must prove he is also orange. So take away one cat from the existing collection of n cats and replace it with the new cat. But we already proved that any n cats are all orange, so because the new cat is in the collection he must also be orange.
The theorem is true!
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When the space ship is 1 light year away, the aliens fire a missile at Chris’ bucket at warp speed 2.06 (2.06 times the speed of light). When will the missile hit its target?
(Answer: Chris’ bucket mysteriously blew up last May.
How did you know that? It made the news.....?
(Dont let out the secret of my time machine, BTW)
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You dont work for a political candidate, do you???? :noshake:
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My cat was orange way before that! I think my cat came first...
LOL! By the way, I think your "proof" should be used as a tool in math classes to teach critical thinking.
It does prove that all orange cats named Felix who are orange are orange and named Felix!
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- Jan 17, 2014
No, my point was not to prove that all orange cats named Felix are orange and named Felix, but that ALL cats, again: ALL cats, are orange. Starting with Felix. If your cat is black then the proof from your perspective would prove all cats are black. In general it proves all cats are identical colors. Which leads to parallel universes, where in your Universe all cats are black and in my Universe all cats are orange...
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No, my point was not to prove that all orange cats named Felix are orange and named Felix, but that ALL cats, again: ALL cats, are orange. Starting with Felix. If your cat is black then the proof from your perspective would prove all cats are black. In general it proves all cats are identical colors. Which leads to parallel universes, where in your Universe all cats are black and in my Universe all cats are orange...
Wow...never heard of proof by induction.
"Proofs by Induction. A proof by induction is just like an ordinary proof in which every step must be justified. However it employs a neat trick which allows you to prove a statement about an arbitrary number n by first proving it is true when n is 1 and then assuming it is true for n=k and showing it is true for n=k+1."
That just goes to show that "assume" still stands for "making an a** out of U and ME"
And that cats are pretty good at proof busting!:agree:
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- Jun 21, 2003
When I was ten my Dad tried to teach me the Theory of Relativity, starting with this result. (Dad wasn't a scientist -- he ran the delivery department for a local meat-packing plant -- but he was curious about a lot of things.) My reaction was, "Big whoop! The speed of light is the speed of light. Duh."
It was not until I got to college that I figured out what the big deal was and why Einstein was the greatest genius of the twentieth century and I was an idiot.
The aliens are whizzing by at some velocity v. They throw out a beam of light at velocity 186,000 miles per second. Here is the picture from our earthbound point of reference.
---------------> + ------------------------------>
v + 186,000 mps
= -------------------------------------------------->
186,000 mps
Thus v+c = c, and we conclude that v = 0.
This experiment (the Michelson-Morley experiment of 1887) was done to measure the speed v of the earth as it flew through space (actually, through the supposed "lumeniferous ether"). It turned out that the earth was standing still (v = 0).
Since the earth is not standing still (Copernicus and Galileo, anyway, thought that it wasn't), classical (Newtonian) physics faced a fatal crisis and had to be discarded.
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- Jan 17, 2014
Because the true velocity addition formula is this:
S(v) = (v1+v2) / (1+((v1*v2)/c2))
where c2 = c squared (no superscript option in the editor).
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- Jun 21, 2003
Click on "Go Advanced" at the bottom of the "reply" dialogue box. This gives you subscript and superscript options.
Or by hand, type [sup*] and [/sup*] (delete * ) around the exponent.
E = mc[sup]2[/sup].
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- Dec 4, 2004
When I was ten my Dad tried to teach me the Theory of Relativity, starting with this result. (Dad wasn't a scientist -- he ran the delivery department for a local meat-packing plant -- but he was curious about a lot of things.) My reaction was, "Big whoop! The speed of light is the speed of light. Duh."
It was not until I got to college that I figured out what the big deal was and why Einstein was the greatest genius of the twentieth century and I was an idiot.
The aliens are whizzing by at some velocity v. They throw out a beam of light at velocity 186,000 miles per second. Here is the picture from our earthbound point of reference.
---------------> + ------------------------------>
v + 186,000 mps
= -------------------------------------------------->
186,000 mps
Thus v+c = c, and we conclude that v = 0.
This experiment (the Michelson-Morley experiment of 1887) was done to measure the speed v of the earth as it flew through space (actually, through the supposed "lumeniferous ether"). It turned out that the earth was standing still (v = 0).
Since the earth is not standing still (Copernicus and Galileo, anyway, thought that it wasn't), classical (Newtonian) physics faced a fatal crisis and had to be discarded.
See, that is exactly where I have my head stuck up my butt. I need a visual graphic. I need to re-watch Carl Sagon's "Cosmos". When the aliens fly by the earth in their '57 Chevy going 2/3 the speed of light, and turn on the headlights, in the frame of reference of the earth, my mind wants to say we see the photons flying at C plus 2/3 C. Which cant be right. Works for slow speed things....not for light.
Its a bit like Euclidean geometry. It is not truth, but it is convenient.
That darned Einstein......
At least I finally figured out why this time of year the sunset and sunrise both get later on any given day until January.
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- Aug 1, 2011
It's been a wet month indeed. It's been raining in the Yakima Valley -- but Sunshine today! YAY!
I've been thinking of taking a calculus class. For fun.
You know there must be medication available to address that urge.
Just saying...
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- Jun 21, 2003
Here’s why we need calculus. We are standing on the seashore watching a boat sail past. A sailor on the boat weighs herself: 110 pounds. Now we weigh her as she sails past: 110.000000000000016 pounds.
Not to worry. This is all in accordance with the formula
m = m[SUB]0[/SUB]/squareroot(1 - v[SUP]2[/SUP]/c[SUP]2[/SUP]),
Here m[SUB]0[/SUB] is the sailor’s mass as measured by the sailor, m is the sailor’s mass as measured by us, v is the sailor’s velocity as measured by us, and c is the speed of light as measured by everyone (5.867 × 10[SUP]8[/SUP] knots).
So what?
Well, by calculus the expression on the right can be expanded in a power series in (v[SUP]2[/SUP]/c[SUP]2[/SUP]):
m = m[SUB]0[/SUB] + (1/2)m[SUB]0[/SUB](v[SUP]2[/SUP]/c[SUP]2[/SUP])
+ higher order terms that are negligible when v is small compared to the speed of light.
Multiply by c[SUP]2[/SUP]:
mc[SUP]2[/SUP] = m[SUB]0[/SUB]c[SUP]2[/SUP] + (1/2)m[SUB]0[/SUB]v[SUP]2[/SUP].
Again, so what? Well, (1/2)mv[SUP]2[/SUP] is the formula in classical physics for kinetic energy. Since half of the formula is energy, the other half must also be a type of energy. So call the whole thing E:
E = mc[SUP]2[/SUP].
Now we are just as smart as Einstein.
We are standing on the seashore watching a boat sail past. A sailor on the boat weighs herself: 110 pounds. Now we weigh her as she sails past: 110.000000000000016 pounds.Not to worry. This is all in accordance with the formula
m = m[SUB]0[/SUB]/squareroot(1 - v[SUP]2[/SUP]/c[SUP]2[/SUP]),
Here m[SUB]0[/SUB] is the sailor’s mass as measured by the sailor, m is the sailor’s mass as measured by us, v is the sailor’s velocity as measured by us, and c is the speed of light as measured by everyone (5.867 × 10[SUP]8[/SUP] knots).
So what?
Well, by calculus the expression on the right can be expanded in a power series in (v[SUP]2[/SUP]/c[SUP]2[/SUP]):
m = m[SUB]0[/SUB] + (1/2)m[SUB]0[/SUB](v[SUP]2[/SUP]/c[SUP]2[/SUP])
+ higher order terms that are negligible when v is small compared to the speed of light.
Multiply by c[SUP]2[/SUP]:
mc[SUP]2[/SUP] = m[SUB]0[/SUB]c[SUP]2[/SUP] + (1/2)m[SUB]0[/SUB]v[SUP]2[/SUP].
Again, so what? Well, (1/2)mv[SUP]2[/SUP] is the formula in classical physics for kinetic energy. Since half of the formula is energy, the other half must also be a type of energy. So call the whole thing E:
E = mc[SUP]2[/SUP].
Now we are just as smart as Einstein.
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