Mathematics and geometry functions in art and architecture during the Italian Renaissance because painters needed to figure out how to depict three-dimensional scenes on a two-dimensional canvas. Another way is philosophers and artists were convinced that mathematics was the true essence of the physical world and that the entire universe, including the arts, could be explained in geometric terms.
In The image shows a geometric function which is the linear perspective the horizontal line and vanishing point is used where the sky appears to meet the ground.
The painting I found to describe mathematical and geometric functions in art is The visual pyramid & Alberti’s “open window”
The geometric function shown in this painting is linear perspective. Alberti used the common knowledge of a visual pyramid to understand perspective. He described the visual pyramid as “…a figure of a body from whose base straight lines are drawn upward, terminating in a single point. The base of this pyramid is a plane, which is seen. The sides of the pyramid are those rays, which I have called extrinsic. The cuspid, that is the point of the pyramid, is located within the eye where the angle of the quantity” This method is explain with an “open window method”
The painter/viewer is located at the peak of the pyramid. When looking from the peak through the pyramid, you can see lots of different planes cutting through the image plane. Some planes are parallel to the cutting edges, others are perpendicular, transversal, or horizontal. When projecting these lines on the image plane, you get the correct perspective projection. The perspective correct image comes into being by a linear projection from the base plane of the pyramid onto the image plane.