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THE MATHEMATICS BEHIND A GASTROPOD SHELL In nature, there are some patterns that repeat itself. Spirals are the one of the patterns that are found in nature enormously. The spirals have common and cosmic appeal to human beings because it is beautiful and mysterious. They are found in the plants, animals, earth and galaxies in other words all around us. Mathematics can explain the logarithms, equations and sequences of the patterns in the spirals (Original Beauty, 2009). Some famous mathematicians categorize the type of spirals. The type that I will mention is logarithmic spirals or known as equiangular spiral since any radius vector makes the same angle with the curve. If we state this equation in parametric form, X= r cos θ= a r cos e bθ Y= r sin θ= a r sin e bθ y r 0 x Descartes was the first person who studied logarithmic spirals in 1638 (Eric Weisstein, 2002). The logarithmic spiral has a polar equation as r = ae bθ ; where r is the distance from the origin, θ is the angle from the x-axis, a and b are the constants. 32 THE CLAPPER 2016 - 2017 To identify whether my shell is logarithmic or not, I first placed the shell picture on a coordinate system in GSP. Using coordinate system helped me to find coordinates of the points on the shell. As seen in Figure 1, the shape I got was a spiral but not sure what kind of spiral it is. The next step that I followed was noting down the coordinates of the points that I labelled, as in Figure 2. Then, I calculated the distance from the origin because it gave me the radii. To find whether the spiral is logarithmic or not, I first figured out the relationship between the angles and the radii. I found the radii by the formula of distance from the origin and I found the angles using the formula: X= r cos θ and Y= r sin θ.