# Mathematics

### Day 286 – Torus conformations of 7_1

Day 286 – Torus conformations of 7_1 1024 768 mathgrrl

Today we have two torus knot conformations of 7_1. A torus knot is one that can be drawn on the surface of torus (“inner tube” shape) without intersecting itself. A…

### Day 285 – Seifert surface of 6_3

Day 285 – Seifert surface of 6_3 1024 768 mathgrrl

Today we continue with the knot conformations collection that we started on Day 266. (See also Day 267, Day 268, Day 269, Day 272, Day 273, Day 275, and Day…

### Day 276 – Petal conformation of 6_2

Day 276 – Petal conformation of 6_2 640 480 mathgrrl

Today is my favorite from the 3D-Printed Conformations of Knots through 7 Crossings series that my Math 297 students developed last semester in the JMU 3-SPACE classroom. It’s a petal knot…

### Day 273 – Lissajous conformation of 5_2

Day 273 – Lissajous conformation of 5_2 640 480 mathgrrl

Today’s knot is 5_2, the three-twist knot, in a Lissajous conformation. The cool thing about this model is that from each side, the knot looks like a wavy cosine function: Thingiverse link: http://www.thingiverse.com/make:80103…

### Day 272 – Lattice conformation of 5_1

Day 272 – Lattice conformation of 5_1 640 480 mathgrrl

The cinquefoil knot 5_1 is one of two 5-crossing knots. The shape we chose for this knot is a  lattice conformation, which means that it follows only perpendicular directions in…

### Day 269 – Minimal stick conformation of 4_1

Day 269 – Minimal stick conformation of 4_1 640 480 mathgrrl

The figure-eight knot 4_1 is the only four-crossing knot, and it is usually drawn like the white knot on the left in the figure below. It is also the only…

### Day 268 – Tritangentless conformation of 3_1

Day 268 – Tritangentless conformation of 3_1 640 480 mathgrrl

The trefoil knot 3_1 is the only three-crossing knot, which means that every other knot that can be drawn as a projection in the plane with three crossings (and no…

### Day 267 – Crazy conformation of 0_1

Day 267 – Crazy conformation of 0_1 640 480 mathgrrl

Today we’ll start going through the knot conformations in the series we introduced yesterday. Before we begin, let’s go over some of the basic notation and ideas of knot theory.…

### Day 266 – 3D Printed Conformations of Knots

Day 266 – 3D Printed Conformations of Knots 1024 768 mathgrrl

The final project for this semester’s MATH 297 – Knot Theory Research and 3D Printing course was to research and print a set of interesting knot conformations for the first fifteen knots…

### Day 265 – Cairo and prismatic pentagons

Day 265 – Cairo and prismatic pentagons 640 480 mathgrrl

Today we fix our fail from Friday (Day 263), and print Cairo pentagons and prismatic pentagons from data kindly provided by Frank Morgan’s student Maggie Miller at Williams College. I have…