Recent content by damo_clark

I have learned that the kinetic energy of a moving object is equal to its mass multiplied by it's velocity squared, divided by 2. If I takes off in my 2 million kg spaceship from rest to 1 million metres/second, I have calculated from this formula that I will need 1 million, million, million...

I haven't solved this problem but can suggest a method which might solve it. 1. I would first generalise the problem to finding the number of ways any number can be represented by smaller integers such that the even integers occur an even number of times. 2. Write a computer program to...

The "Euler Summation Formula" might give you some insight to why the Bernouli numbers pop up in this formula. The term \zeta (-r) is just \frac{B_{r+1}}{r+1} for a positive integer value of r. Another formula that will compute this sum for a positive integer value of r is ...

Structure of numbers part 2 Thank-you for you points Dodo. I assume that the prime factorisation can only be expressed uniquely. For example the unique factorsation of 16 =2^4, not the other solutions shown below eg 2^4 = 2^3 2^1 = 2^2 2^2 = 2^1 2^1 2^2 = 2^1 2^1 2^1 2^1 Its...

Initially I defined 1 as "a", ie. ^{0}a = 1 ^{1}a = 2 ^{2}a = 3 Therfore 1 = a 2 = 2^1 = ^{1}a^1 = ^{a}a^{a} 3 = ^{2}a^1 = ^{^{a}a^{a}}a^{a}. However, it became redundant. The above assumes that if there is not a exponent, or lefthand superscipt, it is 0. Normally...

Now the first prime number 2, can be just expressed as "a". The superscript is ignored just as x is the same as x^1 . 2 = a 3 = ^2a but 2 = a, therefore 3 = ^aa 4 = 2^2 = a^a 5 = ^3a but 3 = ^aa , therefore 5 = ^{^aa}a 6 = 2 * 3 = a ^a \times a 7 = ^4{a} but 4...

I have an idea I'd like to share on this forum about the structure of numbers. I don't have a question as such but am interested to get some feedback on wheather my idea makes sense or if it's been addressed before, or maybe ways to extend on my thoughts. I begin by defining the nth prime...

Thanks Doc Al, I often thought it was just my bad luck that when I dropped a piece of buttered bread it more often that not, landed face down. Now I can blame the laws of physics. I feel much better :)

Thanks Russ, I thought that might be the reason. Just a follow up question... If I spun a wheel in space, say a bicycle wheel, would it keep spining in the initial plane that I set it in motion. I noticed, when fixing my bicycle, that when I spun the wheel and held it at the axel, I could feel...

I was recently casually tosing a fork in my hand so it completed a 360 degree rotation with the handle landing back in my hand. I noticed that everytime I did this, the fork returned to my hand upside down (ie facing downwards). So it took a 720 degree rotation for it to come back in my hand the...

The golden ratio can be found by solving the following problem : Find two numbers that have a difference of 1, and when multiplied together equal 1. The numbers are 1.61803... and .61803... ; the golden ratio being former. Another way to find the golden ratio is to use the Fibinachi...