Everyday Mathematics: Humanoid

  The fingernail, specifically when grown out to a longer length, resembles the square root of a parabolic function. The nail creates a shallow curvature which curls against itself at the ends, reflecting the same shape as that of a square root of a parabola. The square root of a parabola creates this shape as it follows the transformation of y =  √f(x) or (x, √y) , and because of this specific application the nature of square rooting a function is that the transformation line will go larger (outside) of the original parameters, as fractions become larger numbers rather than smaller, creating the curl at the end of the line like the nail does. Other humanoid Square root of a functions: Collar Bone

Three parts of the eye take on the characteristics of a conic function. First, the pupil and iris take on the shape of a perfect circle, the form of a special ellipse, whereas the general shape of the eye encasing the iris, takes on the shape of a horizontal major axis ellipse. with the iris being perfectly symmetrical and circular, as a special ellipse, it is evident that the iris follows the parameters of the equation y^2 + x^2 = 1 , and as the general eye shape follows a structure with a major horizontal axis, it follows the equation of 2y^2 + x^2 = 1 , where the 'y' coefficient will always be larger than the 'x' coefficient.   Other humanoid conic functions: Head and Mouth  (human heads are shaped as a vertical major axis ellipse, and the mouth generally takes on a horizontal major axis ellipse, but can morph into both a circle and a vertical major ellipse)  

Naturally, Fingers have a mathematical nature to their curvature and shape, but more specifically, when regarding the flow of fingers and the space between them, fingers take shape to that of a quadratic formula. Depending on how many fingers you include, and how you decide to start and end, the degree and the leading coefficient will vary, but the foundation remains the same. For example, tracing the middle and pointer finger only, starting up the inner line of the middle finger and following down between the two fingers, then extending up and over the inner pointer finger, and ending down the outside of the pointer finger: a third-degree quadratic function is evident. As we can see, the tracing of the fingers follows the strict pattern of a quadratic function. As shown and described, when tracing the middle and index fingers, there are two humps and the line continues in the same direction before and after the humps, meaning that the image follows the shape of a negative third-degree

 Sofia's curl pattern follows the same structure and flow of a sinusoidal function. There is a clear pattern of symmetry when the shape of the function forms, and we can see that evidently in Sofia's hair. From the photo I took of Sofia's curl, we can see that her hair has a natural dip, followed by a hump, and followed by another dip. This formation of a dip followed by a hump, or a high point to a middle point to a low point to a middle point to another high point (HOLOH), is a direct representation of a sinusoidal function. In Sofia's case, where her hair follows that HOLOH pattern, her curl resembles a Cosine function, which would take the mathematical formula of  y = cos(x) . Other humanoid forms of sinusoidal functions: Knuckles