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Let R be a ring, and let I and J be ideals of R with I subset= J. Then J/I is an ideal of R/I and (R/I)/(J/I)=R/J.

The second-order ordinary differential equation y^('')=y^(3/2)x^(-1/2).

The partial differential equation u_(xy)+alphau_x+betau_y+gammau_xu_y=0.

The Thompson group is the sporadic group Th of order |Th| = 90745943887872000 (1) = 2^(15)·3^(10)·5^3·7^2·13·19·31. (2) It is implemented in the Wolfram Language as ...

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

The larger an arc is, the smaller its radius appears. For example, the three arcs illustrated above belong circles of the same radius.

The three-chord lemma states that in the figure above, l_1+l_2=2lcostheta.

A logical structure which does not assume the law of the excluded middle. Three truth values are possible: true, false, or undecided. There are 3072 such logics.

The sequence of binary digits of the Thue constant, 0.110110111110110111110110110..._2 (OEIS A014578). A recurrence plot of the limiting value of this sequence is illustrated ...

If n>1, (a,n)=1 (i.e., a and n are relatively prime), and m is the least integer >sqrt(n), then there exist an x and y such that ay=+/-x (mod n) where 0<x<m and 0<y<m (Nagell ...