CyberProdigy

Similarities. Both of them are statements based on observations, that seem to be true, but have not been proved or disproved jet. Differences . As explained in G.Pólya and L.Bowden book "Mathematical methods in science", difference is in level of credibility that explanation is based on. Hypothesis is testable, and explanation is based on accepted grounds. Conjecture is proposition based on inconclusive grounds, and sometimes can not be fully tested. Another difference is that conjectures, unlike hypothesis, are used in math. Hypothesis usualy are used elsewhere. If conjecture is proven, it becomes a theorem . Still, the border between two terms remains blurry, and terms sometimes are used as synonyms. For example in math there is a conjecture called ' Riemann hypothesis ', which correctly should be called ‘Riemann conjecture’.

Here is an interesting thing about any matter on the world . For example gold. If you own 1kg gold now. Than after a thousand years you will own a little more than 1kg. Surprised? Don't be. Here is an interesting and tottaly useless facts you never will need to know. But still, it just came into my mind recently. Sun  - the star of our galaxy is producing enormous amount of energy, right? Each second 600 000 000 tons of hydrogen atoms are smashed together with such a speed, that those atoms make 595 000 000 tons of helium atoms. Now the missing 5 000 000 tons are transformed into light energy. Yes. It's funny. 5 000 000 tons of light. No kidding.  And eventually small portion of all this light hits earth surface causing the earth to grow.  Obviously after many, many years earth mass will be bigger, and thus the gravity  it causes also will be bigger. So the very same 1 kg you own now will be heavier on planet earth. If i had some free time i would really like to do some math h...

This morning i was making a tea. I heated up the water, till it started to boil. Usually instead of filling full cup with very hot water, i fill only half, because the rest i fill with cold water, so the tea is not so hot. At the moment, when hot water was poured into the cup, i decided to go to check my email. And then suddenly curious question popped up into my mind. Curious question: In which case the tea will be hotter? If I add a cold water and go for 5 minutes to check my mail or If I go and check my mail for 5 minutes, and when returned, add a cold water The answer is not obvious. Because in first case difference between hot tea and room air is greater, and thus energy will flow faster away from the cup. And on the other hand, in the second case the surface between tea and air is greater, so again it means that energy flows faster away. I did a few calculations to find the answer. It turns out that it is very important what shape is your cup is in. And also the temperature of co...

So i have a problem here. I will probably answer myself to this question after some time, but anyways i will post it here.  So folow the logic i have here. In picture you can see right-angled triangle. Let angle between c1 and h be α. Then c2/h = sin(α) . If α increases then so do length of c2 and length of h. If α=90 degrees then c2 is with infinity length, and so is h=infinity.  so we get that sin(pi/2) = infinity/infinity, which should be undefined, but it is 1. Why?