By Linda Causee
Not just does this e-book current one zero one assorted potholder styles, it exhibits tips on how to mix those patchwork blocks to allow them to be used to make quilts, wallhangings, tablecloths and different patchwork creations.
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Extra resources for 101 patchwork potholders
Work continues to this day on finding a more streamlined and enlightening demonstration of why four colors suffice for all maps in the plane. In a curious twist, it happens that even though maps on the torus require three more colors than those on the plane, it is much easier to prove that every map on the torus can be colored with only seven colors—so much so that Heawood proved it in his original 1890 paper. Exhibiting a map that clearly required seven colors was one part of the proof—it established that at least seven colors were needed, thereby setting a lower bound on the correct answer.
Double row: two consecutive rows in the vertical layout of a bracelet design. In circumference N, a double row has 2N + 1 beads. Structurally twisted: describes a bracelet that does not have a multiple of 2N + 1 beads, where N is the circumference. A structural twist forces a twist of less than 360° in a closed bead crochet rope. Structurally aligned: describes a bracelet that has an exact multiple of 2N + 1 beads, where N is the circumference. Note that a bracelet can be Exploring the Bead Planeâ•‡ ●â•‡21 structurally aligned and also be physically twisted; these are two independent properties.
It is likewise impossible to construct a complete planar graph with no link crossings with more than four nodes since, if we could do so, we could then construct a map from the graph that would require more than four colors to paint. Similarly, it is impossible to construct a toroidal map with more than seven countries that all border one another, and thus it is impossible to construct a complete graph with more than seven nodes on a torus with no link crossings. To gain some intuition for the truth of these statements, see if you can draw a counterexample on paper, such as a complete graph on five nodes with no link crossings.
101 patchwork potholders by Linda Causee