Out of the many things I learned from lecture, the first was about linear perspective. Filippo Brunelleschi was the first person to make a correct formulation of linear perspective. He understood that there should be a vanishing point in which all parallel lines in a plane converge and with that knowledge, he was able to correctly compute the relation between the length of an object and the length of the picture depending on its distance to the plane of the canvas using mathematical principle. He controlled precisely the position of the spectator so that the geometry was guaranteed to be correct.
The second idea I learned about was from Al Haytham who gave the first correct explanation of vision. He showed that light is reflected from an object in the eye and studied the complete science of vision influencing Renaissance artists 300-400 years later.
Next, Piero della Francesca showed that painting has three principal parts which are drawing, proportion, and coloring. Drawing means the outlines and contours contained in a thing. Proportion is the outlines and contours positioned in proportion in their places. Coloring gives colors as shown in the things, light and dark according to the light that makes them vary.
Lastly, Luca Pacioli studied the golden ratio which is the ratio a:b=b:(a+b). He also studied regular and semiregular polygons. His studies were important to architectural design and contributed to one of his famous works known as Divina proportione in which he included figures from his studies.
I believe that the juxtaposition of mathematics, art, and science is like building a house. You need a strong base foundation in order to build a sturdy and effective house. The foundation would be mathematics and the house is art.
Falco, Charles M., and Aimee L. WeintzAllen. "Painted Optics Symposium." N.p., n.d. Web. 24 June 2016.
Frantz, Marc. "Vanishing Points and Looking at Art." N.p., n.d. Web. 24 June 2016.
O'Connor, J. J., and E. F. Robertson. "Luca Pacioli." Pacioli Biography. N.p., n.d. Web. 24 June 2016.
Vesna, Victoria. "Mathematics-pt1-ZeroPerspectiveGoldenMean.mov." Cole UC online. Youtube, 9 April 2012. Web. 24 June 2016. <http://www.youtube.com/watchv=mMmq5B1LKDg&feature=player_embedded>
Watson, Paul F. "Piero Della Francesca." Encyclopedia Britannica Online. Encyclopedia Britannica, 13 May 2016. Web. 24 June 2016.