orthotomic


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orthotomic

[‚ȯr·thə′täm·ik]
(mathematics)
The orthotomic of a curve with respect to a point is the envelope of the circles which pass through the point and whose centers lie on the curve.
References in periodicals archive ?
Step 4: Click on the Caustics and note the following graph, we see that the caustic curve is the set of centers of curvature of the family of orthotomic normals of a given curve relative to O (the red or center dot).
The orthotomic curve of the ellipse relative to the origin, 0, can be shown (see [16]) to be
We plot the original ellipse (in green or inner ellipse), its orthotomic curve (in blue or outer ellipse), and its caustic curve, can be shown to be the curve shown in red (or in the center of the inner ellipse), together in Figure 9.
1], we obtain another orthotomic curve (shown in orange in Figure 5).
As B approaches C, the orange orthotomic curve approaches the black orthotomic curve.
As B [right arrow] C, the orange orthotomic curve [right arrow] the black orthotomic curve.
We now describe how orthotomic curves are used in physics and explore how technological tools accelerate the learning process.
To find the caustic generated by rays reflected by a curve C from a light source O (caustic of C relative to O) is equivalent to finding the evolute of the orthotomic of C relative to O.
1], the orthotomic curve [p(s, 0), q(s, 0)], where s [member of] [0, 2[pi]], is shown Figure 7, which is done by [Maple] (see [15]).
We show the orthotomic curve and its corresponding caustic curve in Figure 8.
3 General Inverses in 3-D, orthotomic and caustic surfaces
0]) as variables, (22) also provides us the orthotomic surface of [S.