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The Klein bottle is a closed nonorientable surface of Euler characteristic 0 (Dodson and Parker 1997, p. 125) that has no inside or outside, originally described by Felix ...

Every Möbius strip dissection of unequal squares can be glued along its edge to produce a dissection of the Klein bottle. There are no other ways to tile a Klein bottle with ...

The Klein bottle crossing number of a graph G is the minimum number of crossings possible when embedding G on a Klein bottle (cf. Garnder 1986, pp. 137-138). While the ...

The Klein graph is a weakly regular graph that is the dual graph of the cubic symmetric graph F_(056)B. The Klein graph is illustrated above in four order-4 LCF notations. ...

If a real algebraic curve has no singularities except nodes and cusps, bitangents, and inflection points, then n+2tau_2^'+iota^'=m+2delta_2^'+kappa^', where n is the order, ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

The partial differential equation 1/(c^2)(partial^2psi)/(partialt^2)=(partial^2psi)/(partialx^2)-mu^2psi (1) that arises in mathematical physics. The quasilinear Klein-Gordon ...

The Klein-Beltrami model of hyperbolic geometry consists of an open disk in the Euclidean plane whose open chords correspond to hyperbolic lines. Two lines l and m are then ...

The metric of Felix Klein's model for hyperbolic geometry, g_(11) = (a^2(1-x_2^2))/((1-x_1^2-x_2^2)^2) (1) g_(12) = (a^2x_1x_2)/((1-x_1^2-x_2^2)^2) (2) g_(22) = ...

In Robert Louis Stevenson's "bottle imp paradox," you are offered the opportunity to buy, for whatever price you wish, a bottle containing a genie who will fulfill your every ...