Adolf Kneser (19 March 1862 – 24 January 1930) was a

German German(s) may refer to: * Germany, the country of the Germans and German things **Germania (Roman era) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizenship in Germany, see also Ge ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. He was born in Grüssow,

Grand Duchy of Mecklenburg-Schwerin The Grand Duchy of Mecklenburg-Schwerin () was a territory in Northern Germany held by the House of Mecklenburg residing at Schwerin. It was a sovereign member state of the German Confederation and became a federated state of the North German C ...

and died in Breslau, Germany. He is the father of the mathematician

Hellmuth Kneser Hellmuth Kneser (16 April 1898 – 23 August 1973) was a German mathematician who made notable contributions to group theory and topology. His most famous result may be his theorem on the existence of a prime decomposition for 3-manifolds. His ...

and the grandfather of the mathematician Martin Kneser. Kneser is known for the first proof of the

four-vertex theorem In geometry, the four-vertex theorem states that the curvature along a simple, closed, smooth plane curve has at least four local extrema (specifically, at least two local maxima and at least two local minima). The name of the theorem derives ...

that applied in general to non-convex curves. Kneser's theorem on differential equations is named after him, and provides criteria to decide whether a differential equation is

oscillating Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...

. He is also one of the namesakes of the

Tait–Kneser theorem In differential geometry, the Tait–Kneser theorem states that, if a smooth plane curve has monotonic curvature, then the osculating circles of the curve are disjoint and nested within each other. The logarithmic spiral or the pictured Archimedea ...

osculating circle An osculating circle is a circle that best approximates the curvature of a curve at a specific point. It is tangent to the curve at that point and has the same curvature as the curve at that point. The osculating circle provides a way to unders ...

Selected publications

* *; *; * *

References

External links

* * 1862 births 1930 deaths 19th-century German mathematicians 20th-century German mathematicians Academic staff of the University of Tartu Presidents of the German Mathematical Society {{Germany-mathematician-stub