MA 391:Mathematics: Composition and Communication1

MA 391: Mathematics: Composition and Communication

Kate Ponto
Fall 2021

Syllabus

Announcements

If you are interested in undergrad math research or mathematical visualizations projects please contact the UK Math Lab.

The class blog can be found here.

Homework

Date	Class topic	What is due
Dec 8	Knots second show and tell	Knots blog post and display card
Dec 6	Do over show and tell	Do over print and display card
Dec 3	Knot polynomials	Do over stl and blog post
Dec 1	Ambiguous objects show and tell	Ambiguous objects print and display card
Nov 29	Links and knot polynomials
Nov 26	Thanksgiving!
Nov 24	Thanksgiving!
Nov 22	Knot colorability
Nov 19	Knots	Ambiguous objects stl and blog
Nov 17	Knots
Nov 15	Knots show and tell and Ambiguous objects	Knots print
Nov 12	Minimal surfaces show and tell and Ambiguous objects	Minimal surface print and display card
Nov 10	Ambiguous objects
Nov 8	Knots (round 1)	Minimal surface stl and blog post
Nov 5	Projection show and tell	Projection print and display card
Nov 3	Minimal surface experiments
Nov 1	Minimal surfaces	Projection stl and blog
Oct 29	Ruled surface show and tell	Ruled surface print and display card
Oct 27	Stereographic projection and surfaces
Oct 25	Fall Break!
Oct 22	Continuity and Stereographic projection	Ruled surface stl and blog
Oct 20	Continuity
Oct 18	Quadric surface show and tell	Quadric surface print and display card
Oct 15	Ruled surfaces
Oct 13	Rotations in 3 dimensional space, ruled surfaces	Quadric surface stl and blog
Oct 11	Level curves show and tell	Level curves print and display card
Oct 8	Quadric surfaces
Oct 6	Quadric surfaces	Level curves stl and blog
Oct 4	Parametric surfaces
Oct 1	Integration over regions in the plane show and tell	Integration over regions in the plane print and display card
Sept 29	Openscad
Sept 27	Level curves	Integration over regions in the plane stl and blog
Sept 24	Center of mass show and tell	Center of mass print and display card
Sept 22	Integration of functions of two variables
Sept 20	Integration of functions of two variables	Center of mass stl and blog
Sept 17	Cross section show and tell	Cross section print and display card
Sept 15	Center of mass
Sept 13	Center of mass
Sept 10	Center of mass	Cross section stl and blog
Sept 8	Washer/Shells show and tell	Washer/Shells print and display card
Sept 6	Labor day!
Sept 3	Surfaces with known cross section
Sept 1	Surfaces with known cross section	Washer/Shells stl and blog
Aug 30	Washers and Shells continued	Printed coins due
Aug 27	Washers and Shells continued
Aug 25	Washers and Shells and trip to the innovation center
Aug 23	On shape and coin printing

Details of prints

Do over

Pick one of the projects we've done so far this semester, redesign and reprint it. (Don't pick the knots project since you didn't have to create the stl andc code.) Your print must

be about 1 and a half cubic inches (It can be larger but don't drive the innovation center people too crazy!)
have structual stability (remove all the supports!)
be a significant improvement over your version 1.

For the blog post you need to explain

how you chose what project to repeat
what you thought needed improments
how you implemented improvements

This blog post must be at least 300 words. For the display card you need to include

which project you are repeating
how your old and new projects compare

Ambiguous objects

Pick two different curves and print an ambiguous object so that two viewers will see the two different curves. Your print must

be about 1 and a half cubic inches (It can be larger but don't drive the innovation center people too crazy!)
have structual stability (remove all the supports!)
clearly illustrate the illusion.

For the blog post you need to explain

how the ambiguous object works
what curves you chose
why you chose the design you did

For the display card you need to include

what curves you chose
do you think they work well

Knots

Print a knot. Your print must

have at least seven crossings
have structual stability (remove all the supports!)

For the blog post you need to

include the crossing number
find a sequence of crossing switches that gives the unknot (this gives a upper bound on the unknotting number
Attempt a coloring. If successful great! If it fails explain what goes wrong.
Compute writhe of your knot
Compute the first two steps of the polynomial Q. You should have four knots.

For your display card include

The crossing number and writhe
an upper bound for the unknotting number

Minimal Surfaces

Make a frame to support a bubble (a minimal surface!). Your print must

fit inside a half full, wide mouth ball jar.
have structural stability (remove all the supports!)
be able to support a bubble

For the blog post you need to explain

what a minimal surface is. You don't need to include all three discriptions we gave in class but you have to include at least one.
the shape of the frame you chose
your best guess of what the bubble on your frame will look like.
why you chose the design you did

For the display card you need to include

the shape of the frame you chose
your best guess of what the bubble on your frame will look like.

Stereographic projection

Pick a design for the plane and use stereographic projection to transfer it to a hemisphere. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have structual stability (remove all the supports!)
be clearly visible when we shine a light through it.

For the blog post you need to explain

what stereographic projection is and what it does
what design you chose for the plane and any challenges you had implementing it
why you chose the design you did

For the display card you need to include

What your design looks like when a light shines through it
How it compares to what you see on the sphere

Ruled surfaces

Pick a ruled surface in 3 dimensional space. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have structual stability (remove all the supports!) and the lines need to be clearly visible
not intersect itself
Do not choose one of the standard surfaces in the annoucement in canvas.

For the blog post you need to explain

what a ruled surface is
what curves you choose to define your surface
why you chose the surfaces and curves you did

For the display card you need to include

what curves you choose to define your surface
any distinctive features of your surface

Quadric surfaces

Pick a quadric surface in 3 dimensional space. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
be at least two pieces of the surface divided by one or more planes. If you only use one plane the division needs to be along a curve that is not a line, a pair of lines, or a single point. (If you divide by more than one plane one of them can be one of these degenerate cases.)
There needs to be an easy way to display the pieces so a viewer can see what is going on.

For the blog post you need to explain

what quadric surface and plane you chose. What the intersection is.
why you chose the surfaces and plane you did

For the display card you need to include

the equation for your quadric surface and the type of surface it is,
the plane you sliced along, and
the equation for the intersection of the quadric surface and plane and the type of quadratic equation it is.

Level curves

Pick a parametrization of a surface in 3 dimensional space. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have at least 8 level curves. More is also fine as long as you can see the distinct curves.

For the blog post you need to explain

how to think about parameterized surfaces and level curves
why you chose the surfaces and parametrization you did

Integration for over regions in the plane

Pick single valued function of two variables. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have at least 20 rectangular prisms. More is also fine as long as the print isn't smooth in the end.

For the blog post you need to explain

how to think about integration for functions defined on regions in the plane
why you chose the function you did
how to compute the volume of your approximation (and compute it!)
how to compute the acutal volume (and compute it!)

Painfully learned insight: slopes get out of control really fast for exponentials and even powers greater than 1.

Center of mass

Pick a solid with known center of mass. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have a unexpected center of mass. (Don't make it so symmetric that the center of mass is in the middle!)
mark the center of mass

For the blog post you need to explain

how to think about center of mass
why you chose the solid you did
how to compute the center of mass of your model (and compute it)

Painfully learned insight: objects that are thinner are easier to balance.

Solids with known cross section

Pick a solid with known cross section to print an approximation of. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have at least ten layers (don't give it so many that it looks smooth - we want to see the layers!)

For the blog post you need to explain

how to think about volumes of solids with known cross section
why you chose the solid you did
how to compute the volume of your model (and compute it)
how to compute the volume of the solid you are approximating (and compute it)

Shells and Washers

Pick a function of a single variable to print a washer or shell decomposition. Your print must

be about 1 and a half cubic inches (tell me your dimensions in your blog post!)
have at least ten washers or shells (don't give it so many that it looks smooth - we want to see the cylinders!)

For the blog post you need to explain

the washer or shell method (talk about the one for your model.)
why you chose the function you did
how to compute the volume of your model (and compute it)
how to compute the volume of the solid you are approximating (and compute it)