Lana Azem, Hannah O'Donnell, Kelsey Rodgers,
Raysa Sylvester
The Hidden Beats of Life

AwardRed Ribbon Award

SchoolGilmour Academy

CityGates Mills, Ohio

TeacherElizabeth Fleming

Selected ResearchHigh Resolution Ultrasound, Brendan Mulcahy

Selected ArtIn the Womb, Amber Furr

Selected LanguageCollecting Echoes, Elizabeth Beam

Our project was designed to raise awareness concerning the amount of time a child spends in the womb of his mother. It signifies the intriciate process of months, weeks, days, hours, minutes, and seconds a child spends in the womb. Most of all we wanted to raise awareness of the important mysteries of life. --Lana Azem

My submission is an essay which outlines the contribution math makes to the rhyme scheme of a villanelle. I calculated the probablility of the words containing the letters it, at, et, ut, or ot in Elizabeth Beam’s poem, "Collecting Echoes." By repeating words which include those letters such as "slit" and "shot," Elizabeth’s rhyme scheme became an intricate and artistic testament to the medical research of Brendan Mulcahy. Included in my submission is a chart detailing my findings. --Hannah O'Donnell

Our project describes the time that a fertilized egg spends in the normal 9 months of pregnancy. We found out how the different parts of math can take us from years to seconds. We used different algebraic equations such as cross canceling.
--Kelsey Rodgers

In the science portion of the experiment, we found the y-maximum, y-minimum and where the greatest pulse echo occurred for the pulse echo graph. For the Second graph, we also found the y-maximum and the y-minimum. We connected this information to Mulcahy’s experiment and how it is important to his project. --Raysa Sylvester

MATH IN SCIENCE: Brendan Mulcahy did research on high resolution ultrasound where "high frequency ultrasonic transducers are used to diagnose intravascular diseases" (Brendan Mulcahy). Lateral and axial resolution were used to determine which resolution would be better for which circumstance. Axial resolution has an inverse relationship to the frequency of the transducer (the sender and receiver of sound waves) depending on how large the patient is. For a smaller patient, they would need a lower amount of frequency since they would not need as much penetration. Lateral resolution, on the other hand, is proportionally affected by the frequency. The higher the frequency, the greater the lateral resolution. In his experiment, he provided results which included two graphs and a data table. In the Pulse Echo graph, the maximum y-value was 40 and the minimum y-value was -20, giving a range of 60 in the voltage during the greatest pulse echo which occurred between 5.40 and 5.45 seconds. In Mulcahy’s second graph, the first harmonic parabola had a maximum y-value of -1.5 and the location of the maximum is (0.01, -1.5). The fundamental parabola had a maximum (0.01, 0). First Harmonic parabola and Fundamental parabola are essentially the same graph except the Fundamental parabola is shifted up vertically by 1.5. Lateral resolution and axial resolution have influenced Mulcahy’s findings because they are both used for different things. In his graphs and data, he focused more on the high resolution to provide an image of coronary arteries. Since Mulcahy used "harmonic imaging to further improve the resolution" (Mulcahy), this leads me to believe that he concentrated on lateral resolution to help him further his research since harmonic imaging allows a lower frequency pulse to be picked up and sampled at a higher frequency. Therefore, low frequency allows greater penetration and high frequency provides better resolution.

MATH IN ART

MATH IN LANGUAGE: A villanelle is a poem with a very complex rhyme scheme. Elizabeth Beam’s villanelle, "Collecting Echoes," was constructed using a large amount of words with the characters it, et, ot, at, or ut in succession within them. These words, such as the word "slit," which appears multiple times in the villanelle, contribute a great deal to the rhyme scheme of Elizabeth’s poem. Applying the mathematic concept of probability, our group calculated how many times such a word appears in Elizabeth's villanelle. See Figure 1 for results.

In total, there is a 19.815% chance that a word from Elizabeth Beam’s villanelle "Collecting Echoes" contains a word with the characters it, et, ot, at, or ut in succession. These words contribute to her overall rhyme scheme in a very significant way and show how mathematics is an integral part of poetry.