Wednesday, October 28, 2015

On God's Number and the Rubik Slide

My master's thesis is an analysis of the Rubik's Slide, a game produced by the Rubik's Company. An analysis has previously been performed by two separate groups of mathematicians and they looked at the produced 3x3 2-dimension version that is available to purchase. My thesis extends the game to a theoretical version of 4x4 2-dimensions. Linked below is my introduction presentation to the "Toy" version that helps identify some key mathematical concepts and theorems prior to the study of the larger and more complex 4x4 version.



I am available for presenting and teaching different levels of learners, from high school through graduate level. This presentation can be adapted for different learners, in it's current state it is designed for honor level high school students but fits very nicely into an Abstract Algebra, Game Theory, or Graph Theory undergrad/graduate level courses.

Problem sets are also available, along with open ended problems that do not currently have a solution.

PPT Slideshow PDF: On God's Number and the Rubik's Slide [last updated: 2015/10/24]

Monday, December 16, 2013

Metric Spaces defined by the Hausdorff Metric

This blog post is a partial requirement of my final project for Mathematical Computing.

Document: Metric Spaces defined by the Hausdorff Metric [PDF]

Matlab Files:


Animation #1 is the well-known Sierpinski affine contraction maps.  It rotates this from 0 to 360 degrees for both theta and phi.
Animation #2 is the Koch Curve affine contraction maps.  It rotates this from 0 to 360 degrees for both theta and phi.

Thursday, December 12, 2013

Social Genius

If you were on Facebook or YouTube over the past 3 days then at some point you probably encountered and maybe even watched the WestJet Christmas Miracle [video - http://bit.ly/1e9d3ZZ].  If you haven't go watch it now and then come back.

Many people's first reaction beyond who is WestJet is wow how generous of the company (it was my initial reaction).  I just happened to see the commercial again when I was on YouTube and noticed that since it was first posted on Dec. 8, 2013 (4 days ago) it has already received 16,654,700 views!  In addition to that it has received 109,383 (0.66%) thumbs up, and only 2,823 (0.017%) thumbs down.

Think about it.  This is 16,654,700 clicks not just basic impressions.  I'm curious as to how much their entire production including gifts actually cost them?  $1.00 per click would be $16,654,700 which seems drastically high but what do I know about the cost of productions.  At $0.10 per click then it would have cost $1,665,470 and that still seems high to me.  If we drop the cost to $0.01 per click then it would have cost us $166,547 which seems like a reasonable budget.

At the rate of $0.01 how much does an acquisition cost them?  To come up with a starting point I chose 700 (0.004%) acquisitions from the 16,654,700 which gives us a rate of $237.92.  I picked 700 going towards the very low end and believe the rate will only go down from there especially considering acquisitions should continue to rise as the click numbers rises.  Now if we only knew how much an acquisition is worth to them?

Seems to be a very effective and affordable marketing and advertising plan that utilizes the power of social media.

UPDATE: On Dec. 18, 2013 the youtube views of the video are at 30,260,070.