anuttarasammyak's latest activity

x-component of this vector increases from 0 to infinity as the path latitude increases from 0 to 90 degree. Right?

The extreme cases I mentioned are when the radius of the smaller semi-circle goes to zero, the larger semi-circle fills exactly half the...

NOT ELEGANT solution The eqation of the circles $$x^2+y^2=R^2$$ $$(x-x_1)^2+y^2=R^2-x_1^2$$ $$(x-x_2)^2+y^2=R^2-x_2^2$$ By subtraction...

@wrobel thanks to your result of the rotation angle of the globe, which is around North-South axis, $$2\pi(1-\sqrt{1-\alpha})$$ where...

It turns out that the system of ODEs in the attachment is integrable in closed form. Thus, the answer to the question is as follows...

The natural numbers form a countably infinite set. You can partition the natural numbers into a finite collection of infinite sets. E.g...

An example of infinite collection of infinite sets is ##\{p^n\}## where p is prime number. We can do similar on n and so on to get...

Let consuming time to infinitesimal part of pass ##dl## be ##dt## with speed ##v##. $$dt=\frac{dl}{v}$$ v depends on where on the path...

What do you mean by slicing numbers? Could you give us some examples?

v<c holds for Inertial Frame of Reference (IFR) s. Two buckets and the spinning platet Earth are rotation systems which are not IFR...

Though I am lazy and awkward in pursuing numerical calculation, I am curious to know it supports my conjecture post #2 or not.

We on planet Earth observe that the stars have rotation orbit of 24 hours period. ##\omega R > c ## for R > 4 * 10^12 m　～　30 a.u...

The insect moving around the latitude circle has angular momentum both in the z-direction and in the direction normal to the latitude...

We draw latitude lines and longitude lines on the globe and set it in a recess for the free rotation with the north pole top initially...

As for movements with regard to trajectory circle, the cases : a. a bettle spins at the circle center b. long snake forms a ring shape...