AwardHonorable Mention Award
SchoolRocky River High School
Selected Research"Music Therapy In Preterm Neonates," Khin-Kyemon Aung
Selected ArtA Sweet Lullaby, Catherine Freed
Selected Language"Music to My Ears," Tyler Bilinovic
We became involved in the eXpressions™ Math program because of the unique opportunities it presented. We all love math and were eager for a chance to work with it outside of the classroom and do something creative with our friends. At the same time we were able to explore scientific research, literature, and art in ways that we had not previously considered. We chose the music project because, through band and recreational listening, music is therapeutic to us in the same way that it is to these wee babies.
-Paige Altemare, Harris Bransch, Patrick Corcoran, Jonathan Lihani, Sean McDermott
Based on the research provided, we decided that we wanted to see the relationship between heart rate and music rate graphically. Based on this comparison, we also wanted to see how the # of apneas while music is playing correlated to what the graphs showed us. We graphed the 3 different speeds of classical music because the research stated set paces for these examples. We compared each to the average heart rate of the babies provided by the research. We used trigonometric functions as models for these patterns. For the music there are 4 beats per cycle.
Putting it all together
The 60 BPM music was the best for the infants based on these results. There were no apneas while it was playing.We believe this is because the beats of the heart and the music line up with a natural pace. The 80 BPM music is very unnatural and is seemingly harmful to health which is reflected by a large number of apneas. The 100 BPM music would, in theory, be better than the 60, but in actuality it was not. It is reasonable that the explanation for this is that a shared beat every 2.4 seconds is too frequent and unnatural for the babies' hearts.
Symmetry in Catherine Freed's A Sweet Lullaby
At a glance, this painting of a baby surrounded by brains and musical notes seems to be devoid of any order or reason. However, after taking a closer look, we found that there are many lines of symmetry in this piece of artwork. The loops of music in the upper left and lower right corners are close to being perfect reflections of each other over the line y = x. The long string of music that makes a loop in the middle of the painting is symmetrical in the line y = x + 4. These lines of symmetry are almost parallel to the line of symmetry in the baby's face! Also, the musical loops in the upper right and lower left corners are close reflections over the line y = -x -1. This is perpendicular to the other two lines of symmetry. These connections serve to tell us that there is a greater pattern between the babies and music in this art work than what may meet the eye. These patterns can be found with the lines of symmetry.
The Mathematics Behind Tyler Bilinovic's "Music to My Ears"
The meaning in this poem does not come solely from its literary elements. By graphing the syllables in each couplet for each stanza, we were able to visually compare the variation in each stanza. Stanzas two and three were very similar to each other. Interestingly, stanzas one and four started out very different and ended with the same number of syllables. This shows how the poem comes full circle. Also, by calculating the average number of syllables and finding the range of +/- three standard deviations from that average, we were able to determine that the poem exhibited a high amount of syllabic control. It is interesting what math can reveal about a piece of literature.