conjugate diameters

The directions indicated by conjugate diameters are taken for space and time axes in relativity.

This diagram included the unit hyperbola, its conjugate, and a pair of conjugate diameters.

Conjugate Diameters in Ellipse at cut-the-knot.org.

In Preston, mothers' external conjugate diameters were similarly unrelated to blood pressure after allowing for birth weight and placental weight.

It is possible to reconstruct an ellipse from any pair of conjugate diameters, or from any bounding parallelogram.

When abstracted to a line drawing, then any figure showing conjugate hyperbolas, with a selection of conjugate diameters, falls into this category.

Conjugate diameters of hyperbolas are useful for stating the principle of relativity in the modern physics of spacetime.

Whatever space and time axes arise through such transformation, in a Minkowski diagram they correspond to conjugate diameters of a pair of hyperbolas.

Each pair of conjugate diameters of an ellipse has a corresponding tangent parallelogram, sometimes called the bounding parallelogram.

The babies' head circumferences correlated strongly with the external conjugate diameters, increasing by 0.17 inches (0.10 to 0.24) for each centimetre increase in external conjugate diameter.

This terminology stems from the use of two conjugate hyperbolas in the pseudo-Euclidean plane: conjugate diameters of these hyperbolas are hyperbolic-orthogonal.

The principle of relativity can be formulated "Any pair of conjugate diameters of conjugate hyperbolas can be taken for the axes of space and time".

Proposition 14 shows how to draw an ellipse through five given points, and Prop. 15 gives a simple construction for the axes of an ellipse when a pair of conjugate diameters are given.

Students making drawings to accompany the exercises in George Salmon's A Treatise on Conic Sections (1900) at pages 165-71 (on conjugate diameters) will be making Minkowski diagrams.

For example, in proposition 14 of Book VIII of his Collection, Pappus of Alexandria gives a method for constructing the axes of an ellipse from a given pair of conjugate diameters.

As E. T. Whittaker wrote in 1910, "[the] hyperbola is unaltered when any pair of conjugate diameters are taken as new axes, and a new unit of length is taken proportional to the length of either of these diameters."