Mathematics!!

[goodbye_farewell]

So I understand the concept of something beginning at c never being able to accelerate above it as it takes infinite energy to accelerate to c in the first place, what's the math behind the faster than light particles not being able to deccelerate below it?

 

If I remember correctly, looking at the equation E = mc^2/sqrt(1-(v^2)/c^2)...  if v>c, then the denominator is imaginary. Sooo resting mass must be imaginary to get a real energy... or something. I am afraid to use Google since I would probably lose the rest of day learning about these things

[goodbye_farewell]

So I understand the concept of something beginning at c never being able to accelerate above it as it takes infinite energy to accelerate to c in the first place, what's the math behind the faster than light particles not being able to deccelerate below it?

Oh, and to actually answer your question, if your particle is traveling faster than c, then E would go to infinity as the particle SLOWS DOWN to c. Same reason why particles can't accelerate up to c. Weird right?

[insanity]

wtf.... This is why I love this place...

 

Also... I hate imaginary numbers...

[Gainsdalf the Whey]

Oh, and to actually answer your question, if your particle is traveling faster than c, then E would go to infinity as the particle SLOWS DOWN to c. Same reason why particles can't accelerate up to c. Weird right?

 

That's really cool. So what happens when you speed up even faster beyond C, the particle gives off energy?

[Oramac]

Oh, and to actually answer your question, if your particle is traveling faster than c, then E would go to infinity as the particle SLOWS DOWN to c. Same reason why particles can't accelerate up to c. Weird right?

 

This is all well over my head, but what about a particle traveling exactly at c?  

[AugustaAdaByron]

You'd divide by zero, in this case you'd need to have zero rest mass. (If I understand correctly)

[goodbye_farewell]

That's really cool. So what happens when you speed up even faster beyond C, the particle gives off energy?

Yup! In theory [emoji14]

[goodbye_farewell]

This is all well over my head, but what about a particle traveling exactly at c?

Yeah, not possible except for massless particles like photons

[Artinum]

This topic is veering away from the pure delights of mathematics and into the dark and murky waters of physics. We'd best get back on track before we start attracting string theorists.

 

Here's a fun one. All prime numbers beyond 2 and 3 can be expressed as either 6n+1 or 6n-1 (where n is a positive integer).

 

It's a simple enough proof. We can express all numbers as one of 6n, 6n+1, 6n+2, 6n+3, 6n+4, 6n+5.

Any number expressed as 6n, 6n+2 or 6n+4 can be divided by two, and is therefore not prime.

Any number expressed as 6n or 6n+3 can be divided by three, and is therefore not prime.

Therefore, only numbers expressed as 6n+1 or 6n+5 can be primes (though not all of them will be, obviously).

And 6n+5 = 6(n'-1)+5 = 6n'-6+5 = 6n'-1.

 

What use is this? It could be helpful if you're creating a prime number generator. Rather than checking every number can be divided by all your previous primes, you can simply check every sixth number, plus and minus one, thus checking only one third as many numbers as doing all of them.

 

(Another good trick for generating prime numbers - you only need to check whether your number N divides by primes p up to the square root of that number. If you find p^2 > N, you don't need to check the later ones, because if a bigger number divides into it then it must be a multiple of a smaller number. And you've already checked those.)

[AugustaAdaByron]

And this just reminded me the Collatz Conjecture.

 

It's very simple to formulate yet has not been proved.

 

Take any number and

- If it is even then divide by 2 (so go from n to n/2)

- If it is odd then multiply it by 3 and add 1 (so go from n to 3n+1).

 

The conjecture states that, if you keep doing it, you will eventually end up to 1.

 

 

If I were to write it in a formal mathematical way (as much as possible given I'm writing in simple text)...

Consider the function 

f(n)= n/2 (for n even) and

f(n)= 3n+1 (for n odd).

For every positive integer n, there exists a positive integer k such that f^k(n)=1.

[goodbye_farewell]

This topic is veering away from the pure delights of mathematics and into the dark and murky waters of physics. We'd best get back on track before we start attracting string theorists.

Easy now!

 

[AugustaAdaByron]

Easy now!

 

 

Jealous much?

[goodbye_farewell]

Jealous much?

Haha not at all. My friends with Math degrees had to dual major to find jobs

[AugustaAdaByron]

Haha not at all. My friends with Math degrees had to dual major to find jobs

 

OK, I'll admit. My PhD may have had parts that slightly deviate to TCS, but they're still Combinatorics.

[goodbye_farewell]

OK, I'll admit. My PhD may have had parts that slightly deviate to TCS, but they're still Combinatorics.

Lol or they stayed in school until they ran out of degrees

[AugustaAdaByron]

Lol or they stayed in school until they ran out of degrees

 

And then found a job at a university, staying in school forever?

[Mark D]

BS and MS in Computer Science here, do I qualify?

 

Here's one I came up with a few years ago, before I trip to Italy (where of course they measure temperatures in Celsius).

 

We probably all know that the formula to convert Celsius to Fahrenheit temperatures is F= (9/5)*C+32, but I've always found multiplying a two digit number by 9 then dividing by 5 in my head more trouble than it was worth, so I came up with this:

 

Double C, subtract 10%, add 32.  Much easier to do in your head, and it's exactly the same formula, because 2C - .1*2C = 1.8C = (9/5)C.

 

One of the problems I ran into in college math was that I'm not a natural mathematician (except for Boolean algebra, which is how I got into computer science), and most math teachers were math majors who generally ARE natural mathematicians.  So while they can DO it, they don't always know HOW they do it, so have a hard time teaching others HOW to do it.

[Artinum]

Easy now!

 

 

That's nothing. My partner studied philosophy, which would probably be even further to the right.

[Estrix]

That's really cool. So what happens when you speed up even faster beyond C, the particle gives off energy?

 

I googled this...I've only just emerged back into the light from the Wikipedia hole I fell down. And I'm no closer to a good answer beyond "some kind of radiation" possibly Cherenkov radiation (but I think that needs a dielectric medium, but maybe not) and you'd also see two images of the particle...I think, a red arriving image and a blue departing image as the speed of the particle would allow Doppler shift to occur across the space of observation.

 

My grasp and understanding of the various explanations I've tried to repeat here is tenuous at best and mostly illustrates the results of falling down said Wikipedia hole. 

[AugustaAdaByron]

[Oramac]

I'm not 100% sure why that's wrong, but it seems that I've committed kitten genocide.  

[Sam Ashen]

wtf.... This is why I love this place...

 

Also... I hate imaginary numbers...

 

Hmm.  I am looking at....

2615 Volts Line to Ground

32.31 Amps

7300 Watts

(per phase)

 

What's wrong with imaginary numbers?

[GoldLynx]

You guyz...I can't keep up. I've created a monster.

Or an angel.

This place is awesome.

Also, Augusta Ada Byron...I'm a math tutor, and that picture is painful. So many students kill so many kittens. I inwardly go into Hulk-mode when this happens.

To the rest of you: I'm only in calc III and phys I, and I've almost no experiences with number systems in other bases. I feel very small.

[Oramac]

7300 Watts

 

I don't know about imaginary, but that translates to about 9.8 horsepower.  

[Gainsdalf the Whey]

This topic is veering away from the pure delights of mathematics and into the dark and murky waters of physics. We'd best get back on track before we start attracting string theorists.

 

Easy now!

 

 

I meant to say this yesterday but never responded. As an engineer, we lie right where chemistry is in being apply physics.

 

Haha not at all. My friends with Math degrees had to dual major to find jobs

 

And this is why I majored in mechanical engineering vs physics.

 

That's nothing. My partner studied philosophy, which would probably be even further to the right.

 

Wouldn't philosophy be further to the left, being applied sociology, the study of the ethics and morals that sociology/theology have developed?

 

BS and MS in Computer Science here, do I qualify?

 

Here's one I came up with a few years ago, before I trip to Italy (where of course they measure temperatures in Celsius).

 

We probably all know that the formula to convert Celsius to Fahrenheit temperatures is F= (9/5)*C+32, but I've always found multiplying a two digit number by 9 then dividing by 5 in my head more trouble than it was worth, so I came up with this:

 

Double C, subtract 10%, add 32.  Much easier to do in your head, and it's exactly the same formula, because 2C - .1*2C = 1.8C = (9/5)C.

 

One of the problems I ran into in college math was that I'm not a natural mathematician (except for Boolean algebra, which is how I got into computer science), and most math teachers were math majors who generally ARE natural mathematicians.  So while they can DO it, they don't always know HOW they do it, so have a hard time teaching others HOW to do it.

 

Never did it for temperature, but going full circle back to fitness, I do it to convert between lb and kg for lifting. lb=2.2*kg= (2*kg)(1.1)=(2*kg)(1+0.1)=(2*kg)(1)+(2*kg)(0.1)=2*kg+(2*kg)(10%)

 

So yeah. If I have to go from kg to lb I double the kg then add 10%. Going the other way is slightly trickier as you have to subtract 9%, then halve it. I do THAT by subtracting 10%, then adding back 10% of whatever I took away, then halving the result of that.

 

100kg to lb is double 100kg (200) plus 10% of the doubled number, so 220 lb.

 

220lb to kg is minus 10% (22, giving 198), plus 10% of the subtracted number (2.2, so 200.2), then halved, so 100.1 kg. Close enough. I typically drop all decimal spots along the way and round to the nearest whole number each time, so there I'd have done (220-22+2)/2=100

 

edit: I've been doing stuff like this since I was a kid. In second grade when memorizing multiplication tables up to 12x12, I realized that for 5 I didn't need to memorize it because I could just cut the number in half and add a zero for even numbers, and for odd numbers, subtract 1, cut it in half, then add a 5 to the end. In third grade, a teacher actually us this rule, and when I said I had figured it out by myself the year before and had been doing it, none of the other kids believed me and thought I was trying to be a smart ass or just look smart. Looking back on it, I was instinctually doing algebra type calculations. Math has always been something that comes easy to me like that.