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An axis is a line with respect to which a curve or figure is drawn, measured, rotated, etc. The most common axes encountered are commonly the mutually perpendicular Cartesian ...

The Cramér conjecture is the unproven conjecture that lim sup_(n->infty)(p_(n+1)-p_n)/((lnp_n)^2)=1, where p_n is the nth prime.

The term "arbelos" means shoemaker's knife in Greek, and this term is applied to the shaded area in the above figure which resembles the blade of a knife used by ancient ...

In the arbelos, consider the semicircles K_1 and K_2 with centers A and C passing through B. The Apollonius circle K_3 of K_1, K_2 and the large semicircle of the arbelos is ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

What is the probability that a chord drawn at random on a circle of radius r (i.e., circle line picking) has length >=r (or sometimes greater than or equal to the side length ...

A roulette is a curve traced by a fixed point on a closed convex curve as that curve rolls without slipping along a second curve. The roulettes described by the foci of ...

Starting with a triangle, draw a circle touching two sides. Then draw a circle tangent to this circle and two other sides. Continue in the same direction. The result is a ...

The term "vesica piscis," meaning "fish bladder" in Latin, is used for the particular symmetric lens formed by the intersection of two equal circles whose centers are offset ...

Andrica's conjecture states that, for p_n the nth prime number, the inequality A_n=sqrt(p_(n+1))-sqrt(p_n)<1 holds, where the discrete function A_n is plotted above. The ...