#calculus

The development of geometry began by measuring the world as discrete objects. Moving beyond measuring nature, it evolved into reasoning, calculation, and mathematics. Platonic solids were one of the most elegant and beautiful ideas reached by geometry. Pondering why there are only five of them was a tribute to collective human intelligence. Earlier in this blog, we modeled polyhedra, like the Platonic solids, using geometric construction methods. This process was like solving a puzzle. To construct a point whose distances…

Below is the first paper of my son, Mete Yazar. It is about a mathematical and geometric exercise of calculating the surface area of an arbitrary shape (a classical guitar’s body panel). He did a good job in utilizing Bezier/de Casteljau curves and generating the parametric equations of the piecewise curve. I helped him to validate the results by using rhinoceros CAD software. Therefore, it seems that his calculations are correct. In this paper, we attempted to calculate a guitar’s…

Curvature can be roughly described as how much a curve is “turning” at point a P. We place two “very” close tangents and measure the difference between them. The closer these tangents are, the more precise our approximation would be. An osculating circle is a tangent circle that has the same curvature as the curve at point P. The larger the circle, the more “flat” the curve is. An infinitely large osculating circle means the curve is linear at point…

Yes, interesting topics started to reveal themselves, when I dig into the function curves, especially in the parametric representation. The first interesting application is the “derivative”. Nobody in high school told me that the derivative of a function at a given point gives the slope of the graph at that point. Moreover, it is possible to convert the slope value into an angle in degrees, showing the angle of the tangent line to the x-axis at that point. They are…