Related papers: Golden Section and the Art of Painting
Much has been written about the golden ratio $\phi=\frac{1+\sqrt{5}}{2}$ and this strange number appears mysteriously in many mathematical calculations. In this article, we review the appearance of this number in the graph theory. More…
The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…
The golden mean, Phi, has been applied in diverse situations in art, architecture and music, and although some have claimed that it represents a basic aesthetic proportion, others have argued that it is only one of a large number of such…
Hawley-Dolan and Winner had asked the art students to compare paintings by abstract artists with paintings made by a child or by an animal. In 67% of the cases, art students said that the painting by a renowned artist is better. I compare…
The problem of the universal form of the size spectrum is analyzed. The half-widths of two wings of spectrum is introduced and it is shown that their ratio is very close to the golden fraction. In appendix it is shown that behind the golden…
This paper explores the Fibonacci sequence and the Golden Ratio as organizing principles for visual composition and abstraction in painting. The author shows how recursive proportional systems, long associated with natural growth and…
The sizes of canvases and stretchers for oil painting have been standardized in France in 19th century and widely accepted in many countries in Europe as well as in Japan so far. These standard sizes do not follow the golden ratio and porte…
This research extends a method previously applied to music and philosophy,representing the evolution of art as a time-series where relations like dialectics are measured quantitatively. For that, a corpus of paintings of 12 well-known…
Motivated by the study of the crossing number of graphs, it is shown that, for trees, the sum of the products of the degrees of the end-vertices of all edges has an upper bound in terms of the sum of all vertex degrees to the power of…
I report the results of the test, where the takers had to tell true masterpieces of abstract art from the fakes, produced by me. I describe each picture by the fraction of the test takers, who selected it as a masterpiece. When I compare…
A coloring of a graph is an assignment of colors to its vertices such that adjacent vertices have different colors. Two colorings are equivalent if they induce the same partition of the vertex set into color classes. Let $\mathcal{A}(G)$ be…
In this paper, we analyze a sample of clippings from paintings by the late artist Bob Ross. Previous work focused on the qualitative themes of his paintings (Hickey, 2014); here, we expand on that line of research by considering the…
Art is the ultimate expression of human creativity that is deeply influenced by the philosophy and culture of the corresponding historical epoch. The quantitative analysis of art is therefore essential for better understanding human…
It is conjectured that there is a converging sequence of some generalized Fibonacci ratios, given the difference between consecutive ratios, such as the Golden Ratio, $\varphi^1$, and the next golden ratio $\varphi^2$. Moreover, the graphic…
The artistic style of a painting is a subtle aesthetic judgment used by art historians for grouping and classifying artwork. The recently introduced `neural-style' algorithm substantially succeeds in merging the perceived artistic style of…
In the words of the twentieth-century British mathematician G. H. Hardy, "the human function is to 'discover or observe' mathematics" (1). For centuries, starting from the ancient Greeks, mankind has hunted for beauty and order in arts and…
A proper coloring of vertices of a graph is equitable if the sizes of any two color classes differ by at most 1. Such colorings have many applications and are interesting by themselves. In this paper, we discuss the state of art and…
Quantitative analysis of visual arts has recently expanded to encompass a more extensive array of artworks due to the availability of large-scale digitized art collections. Consistent with formal analyses by art historians, many of these…
This paper makes the first attempt to introduce the tools from computer graphics into the art pricing research. We argue that the creation of a painting calls for a combination of conceptual effort and painting effort from the artist.…
Based on artistic interpretations, art professor Christopher Bartlett (Towson University, USA) suggested introducing a new mathematical constant related to the golden ratio. He called it the chi ratio, as chi follows phi in the Greek…