Ropes can have knots {rope, knot}.
Deformations cannot make circles from loops {knot, rope}| {Alexander polynomial} {HOMFLY polynomial} {Jones polynomial} {Kauffman polynomial}.
Knots {love knot} can be like ribbon bows.
Three rings {Borromean rings} can overlap, so that no pair of rings has a link but just overlaps, but the three rings cannot separate because each third ring passes through overlapped region of the other two.
A ring can pass through another ring so the rings cannot separate {link}.
Twist one ring to make loop and pass ring through loop {trefoil knot}.
Twist one ring to make two loops and pass other ring through the loops so the rings cannot separate {Whitehead link}. The rings have no net linking.
Knots {bend} can join two ropes at their ends.
Rope part {bight}| can have knot.
To connect two loops or a loop and ring, put loop through ring or loop and then put other loop end, with object, through loop and pull {cinch knot} {clinch knot} {blood knot}.
To attach object to post, loop rope around post, pass under rope, and loop higher than rope {clove hitch}.
To join ends of two ropes so they untie easily, place right-rope end over left rope and pass around and up, pass left-rope end over right rope above place where first loop is, and pass around and out to left {granny knot}.
To link rope and post or loop, pass rope around post or loop, come back to original side, pass around rope, put rope inside loop, and pull {half hitch}.
To shorten rope, tie loop in the bight {sheepshank}.
Knots {sheet bend} can join ropes to middles of other ropes.
To slide loop along rope, make loop, put end around rope, pass to loop inside, pass over small loop, and pass through to make knot {slipknot}.
To permanently join ends of two similar ropes, unravel rope threads and intertwine them {splice}.
To join ends of two similar-size ropes, place right-rope end over left rope and pass around and up, pass that end over left rope above place where first loop is, and pass around and out to right {square knot}.
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Date Modified: 2022.0225