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I have been reading about knot theory for some time, and I am constantly struggling to find the bridge number given a knot or even find the knot projection after searching up the bridge number from databases. I am wondering if there are tricks to find the knot projection that presents the knot with the least number of bridges?

SummerAtlas
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  • What's your version of bridge number? Is it the number of bridges in a diagram, or the version where you have a braid closed with caps on the top and cups on the bottom? I find the second version easier when it comes to finding a diagram with minimal bridge number. – Kyle Miller Jun 30 '22 at 17:57
  • @KyleMiller just the number of bridges. or can you explain how to do the second version? I have seen it somewhere before – SummerAtlas Jun 30 '22 at 20:12
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    I found this answer which mentions it. This is the point of view where it's clearer that 2-bridge knots correspond to rational knots. – Kyle Miller Jun 30 '22 at 22:35
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    Also, in this answer you can see how a 2-bridge knot from the second point of view has much fewer crossings than from the first. – Kyle Miller Jul 01 '22 at 02:13

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