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| | Greetings! I am Marvella and I feel comfortable when individuals use the complete title. The preferred pastime for my children and me is to perform baseball but I haven't made a dime with it. For many years I've been operating as a payroll clerk. My family lives in Minnesota and my family members loves it.<br><br>Here is my website home std test kit ([http://tvoi-tyr.ru/?q=node/51679 find out here]) |
| [[File:Orthoptic locus of a circle, ellipses and hyperbolas.gif|thumb|right|Orthoptics of a circle, of some ellipses and hyperbolas]]
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| In the [[geometry]] of [[curve]]s, an '''isoptic''' is the [[Set (mathematics)|set]] of points for which two [[tangent]]s of a given curve meet at a given [[angle]]. The '''orthoptic''' is the isoptic whose given angle is a right angle.
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| Without an invertible [[Gauss map]], an explicit general form is impossible because of the difficulty knowing which points on the given curve pair up.
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| ==Example==
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| [[Image:Isoptic.png|right|thumb|Orthoptic of a parabola]]
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| Take as given the [[parabola]] (''t'',''t''²) and angle 90°. Find, first, τ such that the tangents at ''t'' and τ are [[orthogonal]]:
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| :<math>(1,2t)\cdot(1,2\tau)=0 \,</math>
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| :<math>\tau=-1/4t \,</math>
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| Then find (''x'',''y'') such that
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| :<math>(x-t)2t=(y-t^2) \,</math> and <math>(x-\tau)2\tau=(y-\tau^2) \,</math>
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| :<math>2tx-y=t^2 \,</math> and <math>8t x+16t^2y=-1 \,</math>
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| :<math>x=(4t^2-1)/8t \,</math> and <math>y=-1/4 \,</math>
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| so the orthoptic of a parabola is its [[Directrix (conic section)|directrix]].
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| The orthoptic of an ellipse is the [[director circle]].
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| ==References==
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| * {{cite book | author=J. Dennis Lawrence | title=A catalog of special plane curves | publisher=Dover Publications | year=1972 | isbn=0-486-60288-5 | pages=58–59 }}
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| ==External links==
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| {{commonscat|Isoptics}}
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| * [http://mathworld.wolfram.com/IsopticCurve.html Mathworld]
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| * [http://www.2dcurves.com/derived/isoptic.html Jan Wassenaar's Curves]
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| * [http://mathcurve.com/courbes2d/isoptic/isoptic.shtml "Courbe Isoptique" at Encyclopédie des Formes Mathématiques Remarquables] (in French)
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| * [http://mathcurve.com/courbes2d/orthoptic/orthoptic.shtml "Courbe Orthoptique" at Encyclopédie des Formes Mathématiques Remarquables] (in French)
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| {{Differential transforms of plane curves}}
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| [[Category:Curves]]
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Greetings! I am Marvella and I feel comfortable when individuals use the complete title. The preferred pastime for my children and me is to perform baseball but I haven't made a dime with it. For many years I've been operating as a payroll clerk. My family lives in Minnesota and my family members loves it.
Here is my website home std test kit (find out here)