The apical angle: a mathematical analysis of the ellipse.
BACKGROUND
The elliptical excision is a common surgical procedure. The dermatologic literature predominantly describes an excisional geometry with a 3:1 length:width ratio and an apical angle of 30 degrees.


OBJECTIVE
To analyze the elliptical excision by applying mathematical principles and define the apical angle and its relationship to the length:width ratio.


METHODS
We examined numerous examples of elliptical excisions as presented in the dermatologic literature. We analyzed the geometry of the excisions and defined it mathematically.


RESULTS
The apical angle of a 3:1 elliptical excision is not 30 degrees. The true apical angle varies from 37 degrees to 74 degrees depending on excisional geometry.


CONCLUSIONS
The commonly presented apical angle of 30 degrees is incorrect and does not reflect the true apical angle of elliptical excisions.
Division of Dermatology, Washington University School of Medicine, St. Louis, Missouri, USA.
B R
BR
Moody
J E
JE
McCarthy
R D
RD
Sengelmann
D062109:Dermatologic Surgical Procedures; D003880:Dermatology / Q000379:methods; D006801:Humans; D008433:Mathematics