## Abstract

It is a well-known fact that any smooth closed plane curve with nowhere vanishing curvature has at least four vertices (local extremum points of its curvature). A generalization of this statement for the case of space curves is known as a conjecture of P. Scherk. Here we sketch the proof of this conjecture. (author). 5 refs.

## Citation Formats

Sedykh, V D.
The 4-vertex theorem for convex curves R{sup 3}.
IAEA: N. p.,
1991.
Web.

Sedykh, V D.
The 4-vertex theorem for convex curves R{sup 3}.
IAEA.

Sedykh, V D.
1991.
"The 4-vertex theorem for convex curves R{sup 3}."
IAEA.

@misc{etde_10113309,

title = {The 4-vertex theorem for convex curves R{sup 3}}

author = {Sedykh, V D}

abstractNote = {It is a well-known fact that any smooth closed plane curve with nowhere vanishing curvature has at least four vertices (local extremum points of its curvature). A generalization of this statement for the case of space curves is known as a conjecture of P. Scherk. Here we sketch the proof of this conjecture. (author). 5 refs.}

place = {IAEA}

year = {1991}

month = {Sep}

}

title = {The 4-vertex theorem for convex curves R{sup 3}}

author = {Sedykh, V D}

abstractNote = {It is a well-known fact that any smooth closed plane curve with nowhere vanishing curvature has at least four vertices (local extremum points of its curvature). A generalization of this statement for the case of space curves is known as a conjecture of P. Scherk. Here we sketch the proof of this conjecture. (author). 5 refs.}

place = {IAEA}

year = {1991}

month = {Sep}

}