Heredity Breast and Ovarian Cancer Risk, Graphing Optimism in DNA, Number of Syllables in

AwardWhite Ribbon

SchoolTrinity High School

TeacherNancy Barile

Selected Research

"Pilot Study to Identify Women at High Risk for Hereditary Breast Cancer in a Community Mammography Clinic Population," Randi Michel

Selected Art*Optimism in DNA,* Grace Kelemen

Selected Language

"Una oda a la ciencia/An Ode to Science," Margret Erlendsdottir

*I chose to analyze Grace Kelemen's Optimism in DNA because in class we were learning about finding lines and functions of graphs, so when we looked at this piece of art, the math jumped out at us. We saw that we could graph the artwork and find the functions using line of best fit. We also liked how the artist combined breast cancer with some of its risks, genes, and heredity.*

— Julie Kuilder

*I chose to interpret Randi Michel's results for her pilot study because I knew that I could relate those results to math. Looking at the pie chart, I knew that a circle offered
many different ways to mathematically interpret the results. I was able to find the number of degrees in each risk level of women obtaining heredity breast or ovarian cancer, as well as arc lengths. I found Michel’s work to be interesting because it was a topic that personally interested me.
*

— Alyssa Licker

*I have always loved poetry and short stories growing up, especially ones that make you think. My love of literature made me choose Ms. Erlendsdottir's poem because it discussed the conflicted viewpoints of science, and it definitely would make the reader think. I never enjoyed math class, so when this project came to combine the two, I was a little apprehensive. Although our teachers say all the time, "math is everywhere," I never truly believed it. Taking the time to evaluate a piece of literature using math gave me a whole new respect for the field of mathmatics.*

— Andrea Panzuto

- MATH IN SCIENCE
Randi Michel, a Cleveland Clinic intern, performed a pilot study to identify women at high risk for hereditary breast cancer in a community mammography clinic population. She displayed her results in a graph representing the risks of hereditary breast and ovarian cancer. After reviewing 234 family history reports, she found that 124 of these families had at least one reported case of breast or ovarian cancer. Randi displayed her results as percentages. She found that 28.6% of the women were at low risk, 11.9% were at moderately increasing risk, 12.3% were at high risk, and 47.2% had more than 2 cases of breast or ovarian cancer in their family history.

In our project, we decided to find the angle measures of the pie chart with Randi's results as well as the arc lengths. To calculate the angle measures, we took the percentages and multiplied each one by 360, which is the number of degrees in a circle. After finding the angle measures to be 169.92, 102.96, 42.84, and 44.28, we checked our work by adding the four angle measures together. Our result was that it accurately equaled 360 degrees. We found the angles of low risk and more than 2 cases in a single lineage to be obtuse, while the angles of high risk and moderate risk were acute because they were less than 90 degrees.

The formula to find the arc length of an angle is S= (radius) (angle in radians). Assuming that the radius was equal to 1 unit, for each of the four sections we multiplied 1 by the number of degrees in the angle by pi and divided by 180. Thus our equations appeared as: S=(1)(169.92)(Π/180), S=(1)(102.96)(Π/180), S=(1)(42.84)(Π/180), and S=(1)(44.28)(Π/180). We found the arc length of low risk to be 1.80 units, the arc length of moderately increasing risk to be 0.75 units, the arc length of high risk to be 0.77 units, and the arc length of more than 2 cases in a single lineage to be 2.97 units.

- MATH IN ART
We decided to find the function of the front of

*Optimism in DNA*.We did this by tracing the picture onto graph paper and assuming that where the left and right side of the piece cross is the origin. We named the points and plotted them into a calculator. We knew that the total piece was not a function, so we separated the art piece into three sections in order to graph it: left (blue), top (purple), and right (green). Once we plotted the points for a section, we used our calculators and found the quartic line of best fit. If the line went through all the points, then we would go to the Y= screen and find the function. We rounded to the thousandths place and found the limitations of x. The limitations of x are the smallest value of x plotted to the greatest value of x plotted. We did this process for each of the sections and colored the artwork accordingly.We looked for any symmetry in the artwork, but since the picture was taken on an angle and not straightforward, there was no symmetry. Had the picture been taken straightforward, there could have been y-axis symmetry. Neither angle would have origin or x-axis symmetry.

When trying to find the line of best fit for each section, we originally tried to find it using the quadratic function, but the line did not go through all the points. We then tried the cubic function to find the line of best fit. This line went through more of the points, but still did not go through all and, therefore, was not as close as possible. On our third attempt we decided to use the quartic function and it went through all the points, so we chose to use this function. As we looked at the lines of best fit on the calculator graph, we saw that using the quartic function created a replica of the front of the picture. Neither quadratic nor cubic had come so close to the picture as the quartic function had, so we knew this was the best option for the function of line of best fit.

- MATH IN LANGUAGE
"Una oda a la ciencia/An Ode to Science" is a literature piece written by Margret Erlendsdottir of Hawken School. Her ode was originally written in Spanish, and translated into English. Margret wrote about the various viewpoints of science, both positive and negative. She also discusses two science-based stories that present the differing viewpoints. To evaluate Margret's work, my group and I graphed the number of syllables in each line in both of the versions, compared the graphs, and discussed the data collected.

We used the Microsoft Excel computer program to assist in making the line graphs. The independent variable of the graph was the line number; there were thirty-one lines total in both. The number of syllables per line served as the dependent variable. The different colored lines (Red= Spanish, Blue= English) made it easy to compare and contrast the two odes. We noticed that the Spanish version had noticeably more syllables than the English. The range was found by taking the maximum and subtracting the minimum. The range of the Spanish (13-4) is 9 and the English range (9-2) is 7. Both of the lines have a similar pattern. As the red line increases or decreases, so does the blue. The difference in the lines, besides the amounts, is how drastic these changes are.

Randi Michel

Pilot Study to Identify Women at High Risk for Hereditary Breast Cancer in a Community Mammography Clinic Population