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In geometry, a set of points in space are coplanar if there exists a geometric plane that contains them all. For example, three points are always coplanar, and if the points are distinct and non-collinear, the plane they determine is unique. However, a set of four or more distinct points will, in general, not lie in a single plane.
After the first three points have been chosen, the fourth point will define a non-skew line if, and only if, it is coplanar with the first three points. However, the plane through the first three points forms a subset of measure zero of the cube, and the probability that the fourth point lies on this plane is zero.
Proclus attributes a definition of parallel lines as equidistant lines to Posidonius and quotes Geminus in a similar vein. Simplicius also mentions Posidonius' definition as well as its modification by the philosopher Aganis. [7] At the end of the nineteenth century, in England, Euclid's Elements was still the standard textbook in secondary ...
For the case of orbital transfer between non-coplanar orbits, the change-of-plane thrust must be made at the point where the orbital planes intersect (the "node"). As the objective is to change the direction of the velocity vector by an angle equal to the angle between the planes, almost all of this thrust should be made when the spacecraft is ...
A planar chiral derivative of ferrocene, used for kinetic resolution of some racemic secondary alcohols [1]. This term is used in chemistry contexts, [2] e.g., for a chiral molecule lacking an asymmetric carbon atom, but possessing two non-coplanar rings that are each dissymmetric and which cannot easily rotate about the chemical bond connecting them: 2,2'-dimethylbiphenyl is perhaps the ...
No, it's not the same as "transgender." Here's what the term "nonbinary" actually means.
Non-binary people are also often misgendered, meaning that others may not always use the right pronouns for them. “When people are misgendered, it can be quite a triggering and traumatic ...
Moreover, the motion of three bodies is generally non-repeating, except in special cases. [ 8 ] However, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists an analytic solution to the three-body problem in the form of a Puiseux series , specifically a power series in terms of powers of t 1/3 . [ 9 ]