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The dimension e(G), also called the Euclidean dimension (e.g., Buckley and Harary 1988) of a graph, is the smallest dimension n of Euclidean n-space in which G can be ...

Maximize the distance a Jeep can penetrate into the desert using a given quantity of fuel. The Jeep is allowed to go forward, unload some fuel, and then return to its base ...

Zeno's paradoxes are a set of four paradoxes dealing with counterintuitive aspects of continuous space and time. 1. Dichotomy paradox: Before an object can travel a given ...

The Pappus graph is a cubic symmetric distance-regular graph on 18 vertices, illustrated above in three embeddings. It is Hamiltonian and can be represented in LCF notation ...

The angular velocity omega is the time derivative of the angular distance theta with direction z^^ perpendicular to the plane of angular motion, omega=(dtheta)/(dt)z^^=(v)/r.

The greatest radial distance of an ellipse as measured from a focus. Taking v=pi in the equation of an ellipse r=(a(1-e^2))/(1+ecosv) gives the apoapsis distance r_+=a(1+e). ...

Given a circle, the apothem is the perpendicular distance r from the midpoint of a chord to the circle's center. It is also equal to the radius R minus the sagitta h, r=R-h. ...

An azimuthal projection which is neither equal-area nor conformal. Let phi_1 and lambda_0 be the latitude and longitude of the center of the projection, then the ...

A quantity defined for a conic section which can be given in terms of semimajor a and semiminor axes b. interval curve e e=0 circle 0 0<e<1 ellipse sqrt(1-(b^2)/(a^2)) e=1 ...

The Euclidean metric is the function d:R^n×R^n->R that assigns to any two vectors in Euclidean n-space x=(x_1,...,x_n) and y=(y_1,...,y_n) the number ...