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Meander (mathematics)
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==Open meander== Given a fixed line ''L'' in the Euclidean plane, an '''open meander''' of order ''n'' is a non-self-intersecting curve in the plane that crosses the line at ''n'' points. Two open meanders are equivalent if one can be continuously deformed into the other while maintaining its property of being an open meander and leaving the order of the bridges on the road, in the order in which they are crossed, invariant. ===Examples=== The open meander of order 1 intersects the line once: :[[Image:OpenMeanderM1.svg]] The open meander of order 2 intersects the line twice: :[[Image:Open Meander M2 jaredwf.png|Open Meander M2 jaredwf.png]] ===Open meandric numbers=== The number of distinct open meanders of order ''n'' is the '''open meandric number''' ''m<sub>n</sub>''. The first fifteen open meandric numbers are given below {{OEIS|id=A005316}}. :''m''<sub>1</sub> = 1 :''m''<sub>2</sub> = 1 :''m''<sub>3</sub> = 2 :''m''<sub>4</sub> = 3 :''m''<sub>5</sub> = 8 :''m''<sub>6</sub> = 14 :''m''<sub>7</sub> = 42 :''m''<sub>8</sub> = 81 :''m''<sub>9</sub> = 262 :''m''<sub>10</sub> = 538 :''m''<sub>11</sub> = 1828 :''m''<sub>12</sub> = 3926 :''m''<sub>13</sub> = 13820 :''m''<sub>14</sub> = 30694 :''m''<sub>15</sub> = 110954
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