Mobius

There are plenty of relationships between pi and phi. First of all if you have a circle of diameter phi then the circumference is pi*phi and is known as the golden circle. Ancient Egyptian's wondered about the relationship between phi and pi, their ancient measurement the cubit was about pi/6 of a metre. they also found this was phi squared / 5. to be fair, as mentioned, any number can arbitrarily be made into another number without any special connection. The thing is pi and phi do seem to have some unusual properties. For example the Phibonacci brick (length and heigth phi units, width 1 unit). Now if this brick is placed exactly inside a sphere the radius of that sphere is 1 and the surface are is 4*pi.... Just google all this stuff to find out more....

My goodness Martin..... this proof of infinite prime numbers was done by Euclid many a moon ago.... with regards to the important of large prime numbers and their importance.... just ask a computer security expert.....

Going back to the original post. this is not quantum mechanics..... Quantum mechanics is based on probabilty... However if you think of an infinite universe or a universe that has infinite time... then if something has a non zero probability of happinning then it WILL happen (an infinite number of times). Crazy world we live in.... Many worlds inturpretation indulges in this.....

this is completly vague as you pointed out... 8 is standard for 'normal' paper, but it really depends on what type of paper it is and how you fold it....

Hmmm I prefer to measure heat in Joules. Light is measured by wavelengths and amplitudes as Kyrisch said. The wavelength is related to the frequency as wavelength * frequency = speed. Red and yellow are the low frequencies of (visible) light while blue and violet are the high frequencies of (visible) light.

weight is a force... The force we exert on the ground due to our mass and gravity. In freefall we still have mass but we are weightless as the force is causing us to accelerate.

Okay from a logical point of view. All bulbs are turned on. then every second 1 is switched off. All multiples of 2 are switched off, this means that 2 squared i.e. is off. Now it will be turned on when we come to every 4th bulb. After this these earlier numbers are left alone. now look at the 3rd bulb, this will turn every 3rd bulb off which includes 9. This one will be turned back on when we get to switch every 9th light bulb. All the numbers have a corresponding square number which will be off until it is turned on when it is time to switch that number. All the other bulbs will end up being switched off. This is not so much a mathematical proof but a logical one....

Okay, I wrote a program to map out the results (well the first 100 anyway). It seems that the only bulbs left on are the square numbers... So light bulb 1, 4, 9, 16, 25.... are on while the rest are off. As yet I have no proof...

Actually my original post is incorrect. I over simplified the sum. In the situation of 10 light bulbs only 1 and 4 are on when you are finished. I will work on this some more.

this is a good question and I don't like answers that state the impraticallity of the question when we should only consider the maths. Light bulb number 1 is obviously on, so are all the prime numbers. Lightbulb 2 is off (as you won't be coming back to it after flipping every second bulb), 3 is on, 4 is off... therefore all the odd light bulbs will be ON and all the even bulbs will be OFF.

Well, I didn't think this thread would turn into a discussion on the eath-moon orbital decay, my fault probably for mentioning it in the original post. It does seem that the question of the earth losing energy was a bit more subtle than I had originally anticipated....

Well if 4 of them have to be picked up then there are 2 left, we now group the 4 as 1, so the choices are basically, how many combinations of 3 items can you have....? More to the point how many ways can you rearrange 3 itmes?

OK, so the moon is slowing down and getting further away from the earth all the time. So back to the original question: I am really trying to find out if the world is losing energy overall??? And the questions I raised in the 4th post!

So it would seem from the global warming that we receive more energy from the sun then we re-radiate back into space. So the moon is taking energy from us due to tidal forces. Our magnetic field is losing energy. What about the using ouf our natural resources. If all the energy is converted without escaping into space then the overall energy loss is nill??? therefore nuclear energy and burning of fossil fuels should not effect the earths energy. I am really trying to find out if the world is losing energy overall. Maybe because of the 2nd law Thermodynamics, it is a must that we are losing energy... Also does the internal heat energy of the earth eventually escape the atmosphere?? I know loads of questions....

Just thought I'd get your thoughts on this. Is the earth overall losing energy. It loses energy from tides, however the earth-moon system remains at constant energy. Our magnetic field is losing energy. Are we losing energy in our rotation? We gain energy from the sun but is the loss of this heat energy more or less than our gain....? All responses welcome