Euler Definition and 414 Threads

Hi, I would like to see the resemblance between planet Earth and a spherical top. I draw here the x-convention Euler angles as I know them: 24 hours to complete one complete one revolution around it's own z' axes. And the 23.5° Earth axes revolves around the "sun's z axes" - the line...

Can anyone help me solve the following question. ABC is any triangle. XAB, YBC and ZAC are equilateral triangles formed on this triangle. Prove that AY, BZ and CX are concurrent. In a triangle ABC, the Euler line is parallel to side BC. Prove that tanB*tanC = 3. I just need a hint. I...

Hi I'm told that the the following can be presented as a classic euler question: A farmer goes to marked with 1770 dollars to buy rice and corn. One bag of corn costs 10 dollars and one of rice cost 20 dollar. How much corn and rice can the farmer buy? This can be presented in the following...

I'm sure this is relatively easy, but after an hour or so googling, I can't seem to find the formula for generating terms of the http://steiner.math.nthu.edu.tw/chuan/123/test/euler.htm Is this known by some other name? Maybe that's why I can't find it? Thanks

how could v 'calculate' the orbifold euler char. using String theorists' formula for the same ? For example, i know the Euler char. of S^1/Z_2 is 1, when we identify the x to -x points of S^1(not the antipodal points i.e. dimetrically opposite points, but putting a mirror along the horizontal...

I did solve this differential equation (x^4)y'''' + 6x^3y''' + 9x^2 + 3xy' + y = 0 using Cauchy Euler Equation. I got X^m (m^2 + 1)^2 = 0 I'm not sure how to get the roots of (m^2 + 1)^2. In my calculation I got m = -i, +i, -i, +i when I put m^2 = -1. In the book they have m = (+-)...

If a connected graph has a Euler circuit then this implies that all the vertices of the graph have even degree. Is the converse of this argument true? i.e. If a connected graph only contains vertices of even degree does this imply it contains an Euler Circuit? Could somebody please show me a...

Would you please tell me how to improve Euler's approximation to be better in solving differerential equations ? Can you give me some links to this? Thank you,

I think this will be my new mantra ;) but it is actually related to the question. I want to define the sequence (s_n) where n is natural and whose nth term, t_n, is the sum of the digits of n. I want to do this without using Gauss's modular arithmetic. This may be one of those 'easier said...

A uniform circular disk of mass m and radius a is constrained to rotate with constant angular speed omega abotu an axis making an angle theta with the disk' s axis of symmetry. Find the magnitude and direction of the angular momentum L and the torque tau exerted on the disk by its supporting...

Euler proved that the infinite product 1/1-p**(-s) with p running over all primes was equal to R(s) where R(s) is teh Riemman z function my question is if the product: 1/1-exp(-sp) over all primes would be hte same as summing the series 1+exp(-s)+exp(-2s)+..=1/1+exp(-s) or what would...

can some one explain to me how is taking the logarithm of euler product gives you -sum(p)[log(1-p^s)]+log(s-1)=log[(s-1)z(s)]? my question is coming after encoutering this equation in this text in page number 2...

[SOLVED] Euler 9 point circle I'm doing a project on the nine point circle and i need to know what type of triangle it works with. I tried constructing it but it didn't work with an isoscoles or a obtuse triangle, but a website said it works with all triangles, can anyone help?

Hi Im a bit stuck on the method for Euler Integration. I have the following first order differential equation: dx/dt = (x-at) / (x / a+t) where constant a = 1.0V/s, and initial condition x = 1.0V at t=0s I have a time step of 0.02 and I need to calculate the output voltage at a time...