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Ideas & Experiments

(9)
Doing Math with Python_ Bertrand's Paradox(1) What's the Problem? Above is an equilateral triange and its circumcircle. Let's say the length of a side of the triangle is 'a', and the circumcircle is called 'O'. In this case, what would the percentage of a random chord in circle O's length exceeding 'a'? Expected Answers 1) 1/3 2) 1/4 Using Python Script 1 _ Random X Coordinate Point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 2..
Light and Collision(빛의 충돌현상에 대하여) 보호되어 있는 글입니다.
Ideas on the Universe & the Big Bang 보호되어 있는 글입니다.
Expansion of Kepler's 3rd Law of Planetary Motion Kepler's 3rd Law of Planetary Motion Kepler's 3rd law of planetary motion, aka the law of harmony is that the period of a planet in the same solar system, squared, is proportional to the 3rd power of the orbit radius. Kepler proposed this law after years of calculating through Tycho's massive observation data. Newton later derived the formula from his law of gravity. proof) * in this article, or..
Integral of linear polynomials raised to the nth power A week ago, while caculating maxium distance of projectile with the effects of drag, I faced a problem. To find the velocity function of the projectile related to time, I had to solve an equation involving the inegral of the square of the velocity function. Since the only thing I knew about integration was multiplying ax^n with x and dividing it by n+1, I had no idea how to move on. So, hoping t..
A Theory on the Grandfather Paradox The grandfather paradox The grandfather paradox is a pafradox about time travel that, what would happen if one were to travel back in time and kill his grandfather before the time travler's parants were born? The time traveler's father will not be born because his father, who has been killed, didn't had any children before. This leads to that the time travler himself cannotbe born. This is a par..
Relation between Time and Velocity in Special Relativity The theory of special relativity explains that time and length can be changed depending on the observer's speed. A few months ago, I have struggled with instantly coming out with the answers to easy science questions in special relativity - I had to calculate the change of time everytime I confronted that kind of problem. So I was wondering if there would be any easy and straightforward way of r..
Pattern of palindromes(팔린드롬의 규칙) A week ago I was just listing binary numbers, to see if there's any pattern in them(cause it's fun to do!). After I while, I noticed that there were the same number of palindromes in 1-digit and 2-digit numbers , another number of palindromes in 3-digit and 4-digit numbers, and so on. Palindromes are numbers that have the same digits starting from the front and the back. In other words, the left..