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  1. K

    Basel Problem Integral

    Summary:: Using an integral and taylor series to prove the Basel Problem The Basel problem is a famous math problem. It asked, 'What is the sum of 1/n^2 from n=1 to infinity?'. The solution is pi^2/6. Most proofs are somewhat convoluted. I'm attempting to solve it using calculus. I notice...
  2. K

    I Closest point on a plane to a point near the plane

    Suppose there is a 3d plane z=a*x+b*y+c. Suppose there is a point in space near, but not on the plane. (xo, yo, zo). What is the coordinate (x1,y1,z1) on the plane that is nearest the original point? My attempt uses minimization but the result is blowing up into large answer. I wonder if...
  3. K

    I Geodesics using only 2 variables: 'time' and 'radius from mass'

    *Moving this thread from 'General Math Forum' to 'General Relativity Forum' in order to generate more discussion.* Any object will move through spacetime along its geodesic. Since mass bends spacetime, an object initially at rest near the mass will move towards the mass along a geodesic. It...
  4. K

    I Rotating a vector in 3d

    Suppose I have a three dimensional unit Vector A and two other unit vectors B and C. If B is rotated a certain amount in three dimensions to get vector C, how do I find what the new Vector D would be if I rotated Vector A the same direction by same amount?
  5. K

    I Infinitesimal Movement Along 3-d Geodesics

    I would like to determine how a point (xo,yo,zo) moves along a geodesic on a three dimensional graph when it initially starts moving in a direction according to a unit vector <vxo,vyo,vzo>. So, if I start at that point, after a very small amount of time, what is its new coordinate (x1,y1,z1) and...
  6. K

    I A Money Swapping Curiosity

    I wasn't sure which forum to post this topic to, so feel free to move it, mods. The topic seems to cover a lot of fields of study: economics, physics, statistics, calculus, etc. :) I was listening to a YouTube video the other day, and the speaker presented situation where there are a thousand...
  7. K

    A Differential movement along a curved surface

    I'd like to understand the movement of a particle along the surface of a three dimensional graph. For example, if there is a flat two dimensional plane (z=2 for all x and y), and a unit vector describes its initial direction of movement (<sqrt(2)/2i+sqrt(2)/2j> for example), then the vector...
  8. K

    A An interesting series - what does it converge to?

    I've lately been interested in series and how they converge to interesting values. It's always interesting to see how they end up adding up to something involving pi or e or some other unexpected solution. I learned about the Leibniz formula back in college : pi/4 = 1/1-1/3+1/5-1/7+1/9-...
  9. K

    I Integrating discs to find the gravitational force of a sphere

    I am attempting to prove Newton's shell theorem. There are multiple solutions to this problem, but I am attempting a solution involving adding up the gravitational force of an infinite number of infinitely small disks that are placed together (the discs facing a point mass "m") to form a...
  10. K

    I Heat diffusion into an infinite rod

    I have recently been curious about heat diffusion. If there is space in one dimension with any kind of temperature dispersed throughout, then the heat equation states that the derivative of the temperature with respect to time at any point equals some constant (k) multiplied by the second...
  11. K

    I Gravitational time dilation derivation

    If a beam of light is shot from a fast space ship, it travels a distance c*t1 according to their reference frame. The same beam of light seen from an outside observer goes at an angle and travels a distance c*t2. The distance the space ship travels is equal to v*t2. Using the triangle made from...
  12. K

    A Gravitational Well Position

    Hello, I am trying to find a function x(t) that describes a particle falling into a gravitational well from a certain distance. So, for example, I am trying to figure out the differential equation: F = m*(dx^2/dt^2) = -GMm/x^2. Or simply, dx^2/dt^2=-GM/x^2 or even more simply, x''(t)=-k/x^2...
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    I Solving Qx+ x^P=R

    I am having difficulty solving Q*y - y^P = Q - 1 for y. If P = 2 or 0.5 or 0, I can solve it quadratically. However, I'd like to find a general solution for y. Any tips?
  14. K

    How fast would it feel you are going?

    Consider this, and tell me where my thinking goes wrong. I'm confused. There is a person observing a spaceship launch from earth, and another person on the spaceship. There are space rocks and asteroids stationary with respect to the earth for the spaceship to observe as it flies. The person on...
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