# Integral formula for secantoptics and its application

Witold Mozgawa; Magdalena Skrzypiec

Annales UMCS, Mathematica (2012)

- Volume: 66, Issue: 1, page 49-62
- ISSN: 2083-7402

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topWitold Mozgawa, and Magdalena Skrzypiec. "Integral formula for secantoptics and its application." Annales UMCS, Mathematica 66.1 (2012): 49-62. <http://eudml.org/doc/268064>.

@article{WitoldMozgawa2012,

abstract = {Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieślak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results.},

author = {Witold Mozgawa, Magdalena Skrzypiec},

journal = {Annales UMCS, Mathematica},

keywords = {Secantoptic; isoptic; secant; secantoptic; oval; integral formula},

language = {eng},

number = {1},

pages = {49-62},

title = {Integral formula for secantoptics and its application},

url = {http://eudml.org/doc/268064},

volume = {66},

year = {2012},

}

TY - JOUR

AU - Witold Mozgawa

AU - Magdalena Skrzypiec

TI - Integral formula for secantoptics and its application

JO - Annales UMCS, Mathematica

PY - 2012

VL - 66

IS - 1

SP - 49

EP - 62

AB - Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieślak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results.

LA - eng

KW - Secantoptic; isoptic; secant; secantoptic; oval; integral formula

UR - http://eudml.org/doc/268064

ER -

## References

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