On Poncelet's porism
We consider circular annuli with Poncelet's porism property. We prove two identities which imply Chapple's, Steiner's and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.
Affine invariants of annuli
A family of regular annuli is considered. Affine invariants of annuli are introduced.
Circuminscribed polygons in a plane annulus
Each oval and a natural number n ≥ 3 generate an annulus which possesses the Poncelet's porism property. A necessary and sufficient condition of existence of circuminscribed n-gons in an annulus is given.
Affine invariants of annuli
A family of regular annuli is considered. Affine invariants of annuli are introduced.
On Poncelet’s porism
We consider circular annuli with Poncelet’s porism property. We prove two identities which imply Chapple’s, Steiner’s and other formulas. All porisms can be expressed in the form in which elliptic functions are not used.
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