Number of correct decimal digits of Pi obtained from the sequences A380099 and A380100
References OEIS Foundation Inc. (2025), Entries A380099 and A380100 in The On-Line Encyclopedia of Integer Sequences, http://oeis.org/
Maths, Physics and Apps Blog
A determinantal formula for the number of trees on n labeled nodes
References OEIS Foundation Inc. (2023), Entries A000272, A362679, and A362711 in The On-Line Encyclopedia of Integer Sequences, http://oeis.org/
Vertical semicircular guide uniformly accelerated
Problem text A vertical semicircular guide, with radius and without friction, is constrained to a platform that moves with constant acceleration along the horizontal direction (see figure). A point body of mass , initially...
Conic sections: an introduction from space
The conic sections (or simply conics) are those curves that are obtained as the intersection of the surface of a cone with a plane. Here, we discuss what kind of curves are achieved by varying the characteristics of the plane...
Minimum speed to throw down a parallelepiped
Problem text Let us consider an object shaped as a parallelepiped and placed on a horizontal plane with friction (see figure). In particular, let us suppose that the object has a mass , a...
Fractions LCM: Mathway vs WolframAlpha
What is the Least Common Multiple (LCM) of two or more fractions? Probably, one can ask himself “What do I need this calculation for?” or maybe one thinks that it is equal to the...
Periodic decimal numbers as series: generating fractions
The periodic decimal numbers, like every kind of decimal numbers, have their own generating fraction. In this post, we provide general proof of the method usually used for converting them to fractions. Let us...
Solved problem: a ball moving around a vertical circumference
Solved problem A ball is tied to one end of a string. The other end of the string is held fixed. The ball is set moving around a vertical circumference without friction, and with...
Parabolic reflectors
A parabolic reflector has the shape of a paraboloid of revolution. The latter one is a space surface of equation (see example in the figure below for ), obtained by rotating the parabola of...
