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A smooth manifold with a Poisson bracket defined on its function space.

A cyclic polygon is a polygon with vertices upon which a circle can be circumscribed. Since every triangle has a circumcircle, every triangle is cyclic. It is conjectured ...

Let F(m,n) be the number of m×n (0,1)-matrices with no adjacent 1s (in either columns or rows). For n=1, 2, ..., F(n,n) is given by 2, 7, 63, 1234, ... (OEIS A006506). The ...

An isoscelizer of an (interior) angle A in a triangle DeltaABC is a line through points I_(AB)I_(AC) where I_(AB) lies on AB and I_(AC) on AC such that DeltaAI_(AB)I_(AC) is ...

An octic graph is a regular graph of degree eight. The numbers of simple octic graphs on n=9, 10, 11, ... nodes are 1, 6, 94, 10786, 3459386, ... (OEIS A014378). Examples are ...

A sextic graph is a regular graph of degree six. The numbers of simple sextic graphs on n=7, 8, ... nodes are 1, 1, 4, 21, 266, 7846, 367860, ... (OEIS A006822). Examples are ...

An edge-magic graph is a labeled graph with e graph edges labeled with distinct elements {1,2,...,e} so that the sum of the graph edge labels at each graph vertex is the ...

Any n-dimensional Riemannian manifold can be locally embedded into an (n+1)-dimensional manifold with Ricci curvature Tensor R_(ab)=0. A similar version of the theorem for a ...

A set U has compact closure if its set closure is compact. Typically, compact closure is equivalent to the condition that U is bounded.

A decagon is a ten-sided polygon. Several special types of decagons are illustrated above. In particular, a decagon with vertices equally spaced around a circle and with all ...