The Dynamic Mathematical Display (DMD) is a device that uses a 3x3 grid of pins controlled by motors and potentiometers to visualize 3D graphs in a hands-on, kinesthetic way. Each pin has an RGB LED and can move to different depths and heights according to a 3D equation programmed into the device's control system. The DMD allows users to interact with and understand complex multi-variable equations by manipulating LED colors and graph formations with the movable pins. An evaluation showed the DMD could accurately model simple equations with only 2% error in pin positioning.

1. DYNAMIC MATHEMATICAL DISPLAY
ABSTRACT It is often forgotten students are learning to build a better future. As a group of students, we are looking to create a form of innovative technology that provides a learning experience through two of the most important learning
methods: visual and kinesthetic. To provide hands on learning experience, we have created the Dynamic Mathematical Display (DMD). The DMD is a device with pins placed within a three by three grid. The pins are 150 mm length, 12.5 mm
width, and each controlled by individual motors and slide potentiometers. The dynamic movement of each pin is measured by the potentiometer's linear resistance, which is monitored electronically by a computer program. That program will
engage the pin to move to a given point projected from 3D graph. The main purpose of the DMD project is to create a morphing table that will allow a user to visualize complicated 3D graphs with all their components such as depths and
peaks. These components will be represented by light emitting diodes (RGB LEDs), which are attached to each pin. The LED's are programmed to provide color based on the physical location of the pin at the time according to the projected
graph. Both instructors and students will have the option to manipulate the brightness and color of the LEDs. While the pins provide kinesthetic information to a graph, the LEDs provide additional visual information similar to a topographic
map, enhancing the learning experience of a student by presenting more realistic and information-rich representations of physical models.
INTRODUCTION
HYPOTHESIS
There are multiple methods in which multivariable equations can
be visualized. Many of the traditional methods of visualizing these
complex equations is on a two dimensional format. In order to
display multivariable graphs in a three dimensional format, the
Dynamic Mathematical Display coordinates a three by three grid of
pins to move to different depths and peaks to imitate a three
dimensional model. RGB LEDs are placed inside of each pin to
enhance depth perception of the three dimensional graph.
METHODOLOGY
During the planning of the Dynamic Mathematical Display, it was
challenging to immediately find the right materials to make the
desired apparatus. Initially, the stepper motor was used to move
the pins, however based on the errors received from the prototype
it was clear that a new solution was needed. The final prototype
consisted of the slide potentiometer’s DC motor, and new pin
design.
The control system for the RGB LEDs is consisted of Python coding
language and Raspberry PI microcontroller. The primary control
system for the pins consisted of JAVA, Arduino Uno and coding
platform. Originally, the two systems above were thought to affect
the function of the apparatus, but after several run of both
systems on the apparatus, no conflicts occurred.
SYSTEM ANALYSIS
The leveling position in which the DMD displays the pins ranges
from 0, 50 and 100. Although, the graph formed by the pins could
be interpreted into equations other than the equation originally
input. For proof of accuracy, several equations were calculated
based on ideal modeling versus what the graph would look like in
pins formation. The comparison between the ideal graph and
actual graph formed by the pins has little error margin (FIG 1 and
FIG 2).
The slide potentiometer’s DC motor is controlled by a motor-
shield, an Arduino and Arduino coding language. As the primary
motor for the pins, the potentiometer receives feedback by the
force put on by the weight of the pins. The constructed system
that drives the pin has a total of 98% accuracy and 2% error in
positioning.
COMPONENTS
PINS (FIG 3)
The DMD consists of nine 3D printed pins (150mm length and
12.5mm width). The pins are placed in a acrylic table top with laser
cut to fit this size of the pins.
SLIDE POTENTIOMETER (FIG 6)
The movement of the pins is controlled by slide potentiometer’s DC
Motors. The pins and the motors are connected by linkages. As the
motors have a side to side motion, they are mounted vertically on
acrylic plate. There are three rows of acrylic plates within the
apparatus and three motors on each acrylic.
ARDUINO - MOTOR SHIELD (FIG 5)
The DMD used Arduino Uno to micro control the movement of the
pins. The Arduino Uno works together with three Adafruit motor
shields, which allows the Arduino to drive the motor, controlling
the speed and position the pins.
RGB LEDs – RASPBERRY PI (FIG 3 & 4)
The RGB LEDs are assistive elements of the DMD projection of
mathematical graphs. The lights are controlled by the Raspberry PI.
The coding for this component is done in Python coding language.
CODING METHOD
The controls of the slide potentiometer was programmed in
Arduino coding language. The movement of the pins according to a
mathematical equation is based off of the JAVA coding language.
Frame (FIG 6)
The frame of the apparatus is made out of wood. The total
dimension of the interior frame is 24” by 7.375”. The dimension of
the foot and the top is 9” by 9”.
CONTACT:
Chelsie Zamelis (lead)- suttsigail@gmail.com
Hamzeh Musleh - hamzahmusle7@gmail.com
Ni Nguyen -ni.nguyen107@gmail.com,
Andrew Ruiz andrew.ruiz@gmail.com,
Alexandra Serdyuk- aleeraalexia@gmail.com
Matthew Ferro – mattferro@siu.edu
Michael Madalina - michaelmadalina@gmail.com
San Min Liew - s.liew2977@edmail.edcc.edu,
Christopher Dombrowski - Chdombroski.christopher@gmail.com,
Jesslyn Budiman - J.BUDIMAN0777@edmail.edcc.edu
CONCLUSION
The Dynamic Mathematical Display was able to successfully model
several forms of multi-variable equations. The RGB LEDs worked
very well in enhancing the depth perception of the graph. The
motor system that drives the pin yielded only 2% in error in
positioning. The apparatus provided sufficient examples of tangible
multivariable graphs. However, the three by three grid is too low in
resolution, the DMD can only graph simple equations.
ACKNOWLEDGEMENTS
Tom Flemming (advisor), Engineering Physics
Jason Sawatski, Engineering Department
Patrick Burnett, Engineering Department
FIG 1 : General equation
Z(m,n) = ℬ((x + m)2 + (y + n)2 ) + ∝
FIG 2 : Actual equation
Z(m,n) = 50((x + m)2 + (y + n)2) + 0
FIG 4 : Raspberry PI and circuit board
mounted on acrylic side frame
FIG 3 : RGB LEDs mounted inside of pins
FIG 5: Left, three motor shield mounted on
top of the Arduino Uno. Right, linkages and
pins placed in the acrylic table top
FIG 6 : Dynamic Mathematical Display fully
assembled.