Enjoy 2023 and 2024!
From left to right: Joel Veena, Sam Richards, and Elias Halloran with Elias's Original Origami Designs
Elias H.
I am fair communicator of mathematics although I am not currently doing much math, except for an aluminum powder coated sign of The Geometric Series. Here's me below on the piano for ya while browsing IJK Tutoring.
Contact Me & Think
Email Elias@ijktutoring.com. I do not travel much out of Brooklyn, NY.
want origami? Skip Down.Here's a Catalogue of Metal Cutouts that I made with The Fabricator
Math Subject Qualifications
Algebra 1
Graphing, "FOIL" and factoring are all made approachable by a teacher. I don't have many current problems that I am working on so I cannot be of any institutional use. I would like to follow some of the paths of Erik Demaine to sort of collect some his mathematical ideas. You can find him at http://erikdemaine.org/ . The best I like is to make my mathematical model for a surface and turn it into an sculpture or some type of life sized sculpture
Algebra 2
It is a continuation of Algebra 1 and 
features more applications and problem solving. The student I work with gain a smooth understanding of numbers and counting formulations, which I frame as incrimentations. I LIKE HOW ALGEBRA IS TAUGHT IN A DIVERSE WAY AND ALGEBRA IS FOR ALL TYPES OF PEOPLE. At this level the student needs to be able to solve the problem, "3 consecutive numbers ad up to 63. What are they?".
Architectural Math
For this I recomend two companies called Shapeways and Send Cut Send which should be in buisness for at least the next 5 years. You are able to learn for the fee from these companies, if you want, on a trial basis. You make a design, then comission them using their electronic quoter to execute the production process. For Send Cut Send I suggest you use Inkscape, which is updated regaularly and free for Mac and PC. For Shapeways you also could want to start with Inkscape since it uses low memory. the DXF file from inkscape is converted to an OBJ file in Tinker Cad... from there you use Tinker Cad, which is free. I worked for a metal working company bringing origami designs into fabrication by making estimates of sizings, clearances, material areas, and solid a
ngles (called dihedral angles). My estimations work out elegantly on the first try of assemblage. Recently I HAVE MOVED THIS SCULPTURE INTO THE FAMS BACKYARD.
Calculus
Yep, if you like the putnam this is for you.
During my junior and senior years in college I was a calculus tutor and explained some of the most difficult calculus problems to undergrads achieving great success with students. I explained easy problems and paradoxes such as Gabriel's Horn and The Painter's Paradox, as well as hard problems: for example, integration problems from the Putnam, which is widely regarded most 
prestigious university-level mathematics examination in the world.
In 2020 my feelings are that I will do some mathematical fine art and if my origami can incorporate my calculus experience, that’s perfect.
Discrete Math
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What do I do in the time of 2021 involving discrete math? The answer, is art. I make these clever metal cut out designs and the concept of colorability came up, a concept from discrete math. I came up with the idea of cross hatching or stripes in metal to give me three colors to color with instead of two, being that you normally see metal cutouts on with the metal or off with a hole of some sort. The Halloran's First Surface you see is a specific surface I plotted in a computer algebra system. I also invented it!! It can also be found as a popular origami model.
Geometry
When I do painting I really need to think about layering and forms. I used rectangles in my abstract art an put them in the behind layer, and I used circles made by compass in the behind layer of my paintings too as well.I could feel that sweet feeling of success as I altered this special turtle fold pattern from 34 or so divisions into 20th divisions. It worked quite nicely and I will do the origami design again sometime.
One day I will look back at the success of teaching geometry with a lot of different students, from all levels of mathematical backgrounds.
Numbers on The Miura-Ori Map fold
Cheers the following is from the origami Miura Ori fold I labeled . I have 2 feet. I have 3 kids origami books, I have 5 fingers, 7 is cool. 23 is an age. 29 is a price for restaurant delivery. 31 could be the total number of electrical parts in something. 37 is a great number to look up on Wikipedia. 59 is like a sushi dinner price. 61 could be an age to cherish having good health. 67 is a phone book number of sorts. 71 is the age of friend's parents. It would be interesting if I used my whimsical perception of numbers in a special way, who knows what will happen?!
Trigonometry
Trig will be good to use on some of my upcoming small time metal working projects. I think that with Send Cut Send and some basic Trig I can start making decorated origami facings and maybe even an engraved origami model out of copper. Right now I am thinking that trig is really the prefect subject for a structural engineer... but my metal working project could manifest as my thoughts should be more organized during the holiday season.
About IJK Tutoring
Resources
The I, J, and K of IJK Tutoring
Fold a Cube with Vectors I J and K
Print instructions 
to fold an artistic construction of the vectors I, J and K. After printing you need to cut out the printed area (which is square). When you are done you will have a beautifully elegant seamless cube and and understanding of how to make these cubes out of paper. To fold this cube, use Jeremy Shafer's popular folding sequence for the Seamless Cube. The sequence is available through a video tutorial. During the times of 3OSME these cubes were discovered. Fumiaki Kawahata and others figured out this cube. Their work is perhaps aptly described as a figuration. Please enjoy IJK's adaptive colorization for this model. The folded cube correctly has arrows above I, J, and K which symbolize directions. There are three total and each one is perpendicular to the other two.
This turtle design has taken years of work to perfect, the process was very in depth. 
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