The apical angle: A mathematical analysis of the ellipse

BACKGROUND. The elliptical excision is a common surgical procedure. The der matologic 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 prin ciples 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, T he true apical angle varies from 37 degrees to 74 degrees depending on exci sional geometry. CONCLUSION. The commonly presented apical angle of 30 degrees is incorrect and does not reflect the true apical angle of elliptical excisions.