Wrapping Up

Our last full day at Disney started early for some of us on Tuesday.  A group of seven went to Hollywood Studios for a final couple of rides on the Tower of Terror.  They had a fun time and bid farewell to one of the group’s favorite rides.

The entire class met after lunch in what has become our classroom away from Furman --- Room 440 (a.k.a. Dr. Harris and Dr. Hutson’s common room).  Groups of three each gave presentations on the projects on which they have been working.  Each group had prepared a poster (digital for now, but to be printed back at Furman) containing a description of the project and the findings.  The first two groups spoke about throughput and single rider lines (topics discussed in the previous two blog posts).  The final two groups discussed the third major project of the class.

Making the Rounds

As you may have read on the blog over the last few weeks, the students have been involved in a project that relates to the mathematically well-known Traveling Salesman Problem.  This problem concerns the discovery of shortest routes in a network of locations, and it is known to be very difficult to solve on a large scale.  The students developed networks that modeled the attractions at Epcot’s Future World and in the Magic Kingdom.  Using data collected by hand (and foot!) and from special distance-measuring iPad apps, the students determined all appropriate distances they needed to model these places.  A small group of students generated an algorithm that worked to find strategic routes through these parks.  The algorithm involved distances between attractions, average wait time for the attractions, and the ride times themselves.

Showing Your Work

The poster presentations were very well done.  Everyone was involved at some level with every project, and so each person was able to contribute to the content of the presentations.  The students will present these posters again as part of Furman Engaged (a day celebrating student research) in the spring of 2015.

After the poster portion of the meeting, the students spent some time discussing possible t-shirt ideas for our class.  They were excited about getting a t-shirt to commemorate what has been a great experience for them --- educationally, intellectually, personally, and socially.

The Final Evening

For dinner, the group went to Boma, a well-known restaurant in the Animal Kingdom Lodge.  This was a buffet style feast of food from Africa, and we enjoyed it so much we wished we could be carried out afterwards (some called this a Boma Coma).

After dinner, the group gathered by the pool and presented Dr. Bouzarth with a surprise “Golden Mickey” award --- recognizing the fact that the wonderful experience we all have had (students and faculty alike) would not have been possible without her foresight, inspiration, and dedication to making it all happen.

We finished off the evening by one last trip to the Magic Kingdom --- a fitting way to end the trip as this was where the trip began three weeks ago.  We stayed until the midnight closing and enjoyed being with one another as we experienced the magic that makes up Walt Disney World.

Signing Off

We hope you have enjoyed reading our blog posts over the past three weeks.  If you have read all of them or just one or two of them, we appreciate knowing that others have been interested in what we have been doing. 

There are many people and groups who have made this experience possible.  We appreciate the support of Furman, the Office of Study Away, and the Mathematics Department.  Most of all, we want to end our posts by thanking the families of all of the participants whose contributions of many types made this the wonderful experience that it was.

As they say around here, we’ll see ya real soon!

Sing-a-Long in the Mathmobile

We had a pretty relaxing day today here at Disney.  We had free time in the morning and early afternoon, and several of us spent time working on the big class project of creating an optimal tour of attractions in the Magic Kingdom.  We are working in three teams to complete the project.  

Beginning to create our  network of the Magic Kingdom

Team Waypoint is tasked with determining which nodes (attractions) and edges (walking paths) will be present in the network model of the Magic Kingdom.  They are also determining ‘waypoints,’ which are locations in the park that link attractions.  The use of waypoints allows us to measure the distance from an attraction to the nearest waypoint, and then use the distance between waypoints to determine the distance between attractions.  In this map of our network, you can see the nodes in yellow and the waypoints in pink.  This method prevents us from having to measure the distance from each attraction to every other attraction.

Team Map My Run is working on measuring the distances between attractions and waypoints.  They are using the iPhone app Map My Run to measure distances along sidewalks between attractions and waypoints.  The app’s website has satellite images that allow us the team to calculate distances without having to walk them.

Team Algorithm is working on writing a computer program to calculate an optimal tour through the Magic Kingdom.  The program will take the list of attractions and distances created by Team Waypoint and Team Map My Run as input.  The program will use a genetic algorithm to create an optimal a tour through the Magic Kingdom than minimizes walking distance.  Genetic algorithms are modeled after evolutionary processes, and involve mutating tours and replacing longer tours with ‘more fit’ shorter tours.  We hope to later extend the algorithm to minimize the time spent waiting in line.  However this complicates the problem significantly, since these wait times change throughout the day.

This afternoon we collectively voted to visit Hollywood Studios to experience Disney's "Star Wars Weekend" and to grab another ride what many would argue are the best two rides in all of Walt Disney World. (Tower of Terror and Rock 'n Roller Coaster of course!) It has been very hot here in Orlando, so a later start and a few showers this afternoon and evening greatly helped with the heat. We split up, hitting some highlights including the delicious ice cream shop outside of Tower of Terror and the Toy Story Pizza Palace Arcade. 

The whole group reconvened to watch Fantasmic, a dazzling light show featuring our favorite Disney characters adventuring through the world of Mickey's dreams. Although we got a little wet from the showers, it was a fun conclusion to our day. On the drive back we mustered up enough energy for a dance party and sing-a-long in the mathmobile. Moving from pop to classics to Italian opera to Disney ("Let it Go" of course), Dr. Bouzarth was a trooper to drive the van which was quite literally rocking and maybe even sing along!

Stella and Kate

Coloring and Physics

Hi everybody, Hannah and Kelly here to give you the update on May 22nd, day nine of our trip!  

Coloring and Physics Fun:

Now, we know what you're thinking, they get to go to DisneyWorld every day and now coloring?  Well, that's not quite the case.  Today, Dr. Harris taught the group about a specific set of problems in Graph Theory called colorings.  Colorings are when you take a graph, made up of vertices and edges, and try to "color" each vertex so that no two connected vertices have the same color.  These colorings help to visualize scheduling problems and to determine the fewest number of workers needed for specific intervals.Next, Dr. Bouzarth joined in on the fun and began to explain some of the physics behind our favorite Disney rides.  Included in our lesson was a discussion of forces, conservation of energy, and magnetism.  For example, the Rock ‘n’ Roller Coaster in Hollywood Studios uses both permanent magnets and electromagnets to create the 0 to 60 launch at beginning of the ride. 

Afternoon Park Fun:

After discussing our favorite attractions and how physics played a part in creating the experience, we headed over to Hollywood Studios to see some physics in action.We all headed over to The Voyage of the Little Mermaid, which is a brief retelling of the movie with live preforming, puppets, clips from the movie, and wet water effects. We then split up for a bit while some of us headed over to The Tower of Terror and experience the ride, now equipped with knowledge of how Disney uses physics to make the ride more exciting. When the elevator car drops, it is actually moving to the ground faster than it would if only gravity was pulling it to the ground, which gives the rider that weightless feeling at the top. Another portion of the group headed over to the Animation Studio and to meet Mickey and Minnie. We then all met up again to watch a car stunt show called Lights, Motors, Action, which most everyone enjoyed. After that the group split again and some went and enjoyed some delicious ice cream while others went and rode the Rock ‘n’ Roller Coaster. We then reunited for some friendly competition on Toy Story Mania to end our day.

Tomorrow is Disney’s 24-hour event called “Rock Your Disney Side” where the Magic Kingdom is open from 6AM Friday morning until 6AM Saturday morning. This day at the park will be filled with special events and lots of fun dance parties. A (probably crazy) group is planning to wake up at 4AM to get to the Magic Kingdom early tomorrow before it even opens to be there as the rope drops (and to participate in the “Frozen Family 5k” and hopefully meet Princesses Elsa and Anna from Disney’s movie Frozen).

The Keys to a Mathemagical Adventure

Selfie by our tour guide with another cast member

Hayden and Rahul are back to give you the most recent updates from our mathemagical adventures. 

The Mouse

 

This morning we got to go “backstage” in Magic Kingdom on the Keys to the Kingdom tour given to us by our hilarious tour guide Megan. This signature Disney tour goes behind the magic of Disney World, explaining some of the little known history and secrets of the happiest place on earth. And lucky you, we’re going to share some of these “secrets” with you. One of the coolest parts of the tour was getting to explore part of the Utilidor; that’s right, the Magic Kingdom really does have secret underground tunnels! The Utilidor is the real ground level to the Magic Kingdom that is used by staff and cast members to help maintain the four keys to the Kingdom- safety, courtesy, show, and efficiency. Cast members and characters can use the Utilidor to travel across the park without being seen out of costume or in the wrong “land.” Maintenance use the corridors to quickly transport any require tools or equipment, and Reedy Creek Emergency Services (Disney has to provide their own emergency services due to its size and spread across two counties) can use the tunnels to quickly access guests in need without dealing with crowds above. Part of the Utilidor is also used to vacuum trash collected above into a tunnel that sucks the over 80,000 pounds of trash produced each day to backstage trash compactors.

Students take picture on tour

We also learned interesting new facts about some of the more visible “upstairs” Disney secrets. As you walk down Main Street, you may have noticed some of the writing on the stores’ upstairs windows; this is what Disney World considers its “credits.” When you first walk in and look above the Confectionery, you see Roy Disney’s name. Roy, Walt’s brother and partner, helped start Disney World, taking care of most of the business’s finances. Walt in on the other end of Main Street, above the Ice Cream Parlor since he had a nightly bowl of ice cream. We also learned about the cues they use to transition between the different lands, such as changes in the sidewalk color and texture, different music, changes in decorations, and some less obvious and more symbolic details. For example in Liberty Square, the light-colored stone path throughout this section of the park, symbolizes towns before plumbing where waste was thrown into the street. Each branch of the stone path leads to a bathroom, all of which are technically outside of Liberty Square and in the next land. This is just one of the many details that helps to make the “show” by bringing guests back to pre-twentieth century United States. Overall the tour was an incredible experience, that exposed the hard work and detailed ingenuity needed to create such a magical destination.

The Math
 

The tour was far from the end of our day. We had lunch at the park and then returned to our hotel. After a quick 20 minute break, we were back at work. We had previously been split up into groups and assigned to read mathematical papers and present on the mathematical models they described. These papers related to various problems faced at amusement parks like Disney: optimizing hotel reservations, golf tours and crowd flow.  These were peer reviewed papers published in respected journals, not aimed at undergraduate students. Mirroring last week, we, Hayden and Rahul, had contrasting yet similar experiences here. I, Hayden, am a rising sophomore Chemistry major, so before this I’ve had almost no experience reading mathematics journals. However, each of our groups included students with a wide range of experience with this type of work. Students like Rahul were able to explain some of the math notation and terminology that was new to me, so ultimately, I was able to fully understand the paper I had read. I, Rahul, am a rising senior Mathematics major, and have done Mathematical research both of my previous summers at Furman and have as a result have read a number of mathematical papers. However, reading a mathematics paper on an unfamiliar topic is always challenging, no matter your background, it took time and effort before I had any idea how the model worked. At the presentations today, it was clear that all three groups had put in a good deal of work and displayed a full understanding of the situations being modeled as well as the mathematics behind it: objective function being optimized, the variables and the constraints.

Planning locations of Waypoints

Now that we had shown that we had a solid grasp of how mathematical modeling worked, we finally began what we hope will be our primary project for the remainder of the course. We are going to create our own model for optimizing tours of Disney World. Like with any other project, the key is to start small. The first step is to gather data about a small segment of the park. We will use our data gathered from the Epcot Challenge last Friday as a starting point. We plan to gather more information tomorrow while visiting the park and will combine this with data scraped from the internet. Rather than trying to calculate travel time between every single attraction at the park, we created a set of “waypoints” on the map of Epcot which will form the nodes of our graph. We will only need to know the travel times to the central node. Other travel times can be computed with this data using, for example, Dijkstra's Algorithm. Another advantage of using such a system with waypoints is that it is easily expandable, thus making for a robust model.

The Fun
 

About half the group chose to stay at the hotel this evening, but the rest of us decided to venture back into Disney, this time to Hollywood Studios. This was mostly just for fun, although we did try to test out a few theories we had developed about wait times, with some success. We finished up the night watching the fantastic Fantasmic! show, featuring everything from fireworks and lights to costumed actors and animations projected onto sheets of water. As we left the park, we noticed cast members closing the gates to Tower of Terror and Rock ‘n’ Roller Coaster. Just this morning, Megan had described Disney’s closing process of checking one attraction at a time and moving toward the main exit from there, and she assured us there was no way to hide out over night with this thorough shutdown plan. Dr. Harris, however, seemed to have taken this as a challenge and was working on an algorithm or two to solve this particular problem as we walked out.

Second Day - A Downpour of Knowledge

Hello! Jordan and Annie here to report on our activities for Thursday, May 15^th. Our first full day of Math and the Mouse has been nothing short of a whirlwind of adventures!

Learning Modules

After our long day yesterday, beginning at 5:45 a.m. and ending around 11 p.m., everyone was ready for a good night’s sleep. So, we began our morning today with continental breakfast in the hotel on our own individual schedules and convened as a group at 9:00 a.m. in the common area of Dr. Harris and Dr. Hutson’s room for our first learning module. Dr. Hutson introduced us to linear programming modeling – a key concept for our analysis of Walt Disney World’s operations and physical layout. Linear programming modeling allows us to optimize a function, such as profit margin of a production company or travel time from one location to another in a theme park, while imposing certain constraints, such as limited materials or manpower. In other words, linear programming provides us with a tool to represent a real-world situation mathematically, through a collection of variables and equations, and allows us to find the “best” or most efficient way to accomplish a certain task. Today, our focus was on creating the models, but we will soon be exploring computer software capable of solving even the more complex problems, such as those we will encounter in Disney World. Everyone seemed to really enjoy Dr. Hutson’s lesson and the various real-world examples we worked through together to aid our understanding.

Next, Dr. Harris introduced us to Graph Theory. A graph is a set of vertices (dots) connected by a set of edges (lines). Although this concept seems simple, graphs can become complicated quite quickly, and even a simple question, such as whether or not one can connect all the vertices of a graph without traversing any vertex twice, can be very difficult to answer. However, graph theory will be very important in modeling the different parts of Disney World, since each park is essentially a set of attractions (vertices) joined by a set of walkways (edges). A network model is a graph that represents this type of real-world system and includes data such as travel time and distance. Our group was very engaged during Dr. Harris’ graph theory presentation and is excited to apply this knowledge to model the parks!

Hollywood Studios

After the morning learning modules, we took a quick lunch break and then were off to Hollywood Studios for the afternoon! The weather was a little dreary, but we were prepared for the rain, and not-so-great weather means smaller crowds and shorter lines. Because of this, Dr. Hutson led a small group to ride his all-time favorite attraction, the Tower of Terror, three times in a row, ending with a ride by the entire group. Our excited giggles and screams during the freefalls really spotlighted the fun everyone was having. Afterwards, we were lucky enough to walk onto the other crowd-pleaser, the Rock ‘n’ Roller Coaster, without a wait. Though we discussed that we really wanted to calculate the initial acceleration of the roller coaster (which goes from 0 to 60 miles per hour in 2.8 seconds), we decided to save that for a later day and simply enjoyed the ride.

After these two thrills, we went to Toy Story Mania, an interactive game-ride, which brought out everyone’s competitive side. Dr. Bouzarth scored the most points, but the verdict regarding whether or not she cheated is still out...

Towards the end of our afternoon in the park, we were told we could split up into smaller groups for the remainder of the visit, but, in reality, we twelve students couldn’t help but stick together. Though we’re just two days in, it’s clear that our group is bonding really quickly, which I’m sure will make both classwork and projects  that much more of a positive experience for everyone!

We ended the day with a group dinner at Panera. Earlier today, we were divided up into teams for a fun project we have tomorrow, so, while there, we were able to take advantage of the WiFi and meet with our teams to plan our strategies. It’s safe to say that we’re all looking forward to facing off in what sounds like an intense day of competition tomorrow!