Set of barber

The set of Barbier states that the scope of any of the same thickness of the same width is constant and equal to the circumference of a circle whose diameter corresponds to the width.

The following applies to the circumference of an equal thickness with width : ${\displaystyle U}$ ${\displaystyle b}$

${\displaystyle U=b\cdot \pi }$

Since a circle with a diameter is also an equal thickness with a width , all equal thicknesses with a width have the same circumference as the circle. ${\displaystyle b}$ ${\displaystyle b}$ ${\displaystyle b}$

The sentence was published in 1860 by the French mathematician and astronomer Joseph-Émile Barbier (1839-1889) and is now named after him.

literature

• Günter Aumann : Circular Geometry: An Elementary Introduction . Springer, 2015, ISBN 978-3-662-45306-3 , pp. 219–222
• Christian Blatter : Over curves of constant width . In: Elements of Mathematics , Volume 36, Issue 5, 1981, pp. 105–114
• Ross Honsberger: The Theorem of Barbier. In: Ingenuity in Mathematics , pp. 157-64. Mathematical Association of America, 1970.

Web links

• Eric W. Weisstein : Barbier's Theorem . In: MathWorld (English).
• Barbier theorem in the Encyclopaedia of Mathematics