The golden ratio, approximately 1.618, has been used in various fields, especially art, architecture, and design, since ancient times. Here’s a list of notable works and structures where the golden ratio is believed to have been employed: ### Art 1. **"The Last Supper" by Leonardo da Vinci** - The proportions of the composition, especially the placement of Christ and the apostles, exhibit the golden ratio.

"Relativity" is a famous lithograph created by the Dutch artist M.C. Escher in 1953. The artwork is known for its intricate and impossible architectural constructions that challenge the viewer's perception of reality. In "Relativity," Escher depicts a world where different gravity orientations coexist, allowing figures to walk on multiple planes and surfaces that appear to defy the laws of physics. The composition includes staircases that lead nowhere and figures that interact in seemingly impossible ways.

In biochemistry, the term "response coefficient" can refer to various contexts, but it often relates to the quantification of the response of a biological system or a biochemical assay to changes in certain conditions, such as substrate concentration, enzyme activity, or the presence of inhibitors. One common application of response coefficients is in enzyme kinetics, where the response coefficient can describe how the rate of an enzymatic reaction changes in response to changes in substrate concentration.

Secondary electrospray ionization (SESI) is a mass spectrometry ionization technique that is used to analyze volatile and semi-volatile compounds in the gas phase. It is an extension of the conventional electrospray ionization (ESI) method, which is typically utilized for non-volatile compounds in solution. In SESI, a sample can be introduced as a gas or vapor rather than in a liquid form, which broadens the range of analytes that can be studied.

The Sulston score is a grading system used to evaluate the severity of damage caused by a traumatic brain injury, specifically in the context of head injuries. It was developed by neurologist Dr. Michael Sulston and is primarily used to assess the extent of brain injury in patients who have sustained concussions or other head trauma. The scoring system typically takes into account various clinical factors, such as the level of consciousness, neurological functioning, and the presence of any physical symptoms following the injury.

The Binomial Options Pricing Model (BOPM) is a widely used method for valuing options, which are financial derivatives that give the holder the right (but not the obligation) to buy or sell an underlying asset at a specified price before a specified expiration date. The model was introduced by Cox, Ross, and Rubinstein in 1979 and is based on a discrete-time framework.

The Vienna Series in Theoretical Biology is a collection of publications that focus on the integration of theoretical approaches with biological research. The series is primarily associated with the Vienna Institute of Theoretical Biology and aims to explore complex biological systems through mathematical modeling, computational simulations, and other theoretical frameworks. The topics covered in the Vienna Series often include aspects of evolutionary biology, ecological modeling, systems biology, and the dynamics of biological networks.

Vincent Calvez is a mathematician known for his work in the fields of probability theory and mathematical biology. His research often involves stochastic processes and their applications in modeling biological phenomena.

Vito Volterra was an Italian mathematician, born on May 3, 1860, and died on October 11, 1940. He is best known for his contributions to mathematics, particularly in the fields of integral equations, functional analysis, and mathematical biology. One of his significant contributions is the development of the Volterra integral equations, which are used to describe various physical phenomena.

The Webster equation is a mathematical model used in acoustics, particularly in the field of speech and hearing, to describe the propagation of sound waves in a tube-like structure. It is particularly applicable to the study of how sound travels through the vocal tract, which can be approximated as a series of cylindrical sections.

"Crucifixion (Corpus Hypercubus)" is a notable painting created by the Spanish artist Salvador Dalí in 1954. The work is considered one of Dalí's masterpieces and is emblematic of his surrealist style, which combines dream-like imagery with complex symbolism. In this painting, Christ is depicted on a cross that resembles a hypercube, or tesseract, which is a four-dimensional geometric shape.

Chemical Reaction Network Theory (CRNT) is a mathematical framework used to study the behavior and dynamics of chemical reaction systems. It provides tools to analyze how the concentrations of chemical species evolve over time as a result of reactions. This theory is particularly useful in understanding complex systems, including those that may not remain at equilibrium, such as in biochemical networks or in non-equilibrium processes.

Quantitative analysis in finance refers to the use of mathematical and statistical methods to evaluate financial markets, investment opportunities, and the performance of financial assets. This approach employs quantitative techniques to analyze historical data, assess risk, and develop pricing models, ultimately aiming to inform investment strategies and financial decision-making. Key components of quantitative analysis in finance include: 1. **Data Analysis**: Quantitative analysts often utilize large datasets to identify patterns, trends, and correlations.

The Rate of Return (RoR) on a portfolio is a measure of the percentage gain or loss that an investment portfolio has generated over a specific period of time. It reflects the performance of the portfolio and is a vital metric for investors looking to assess how well their investments are doing.

"Reptiles" is a lithograph created by the Dutch artist M.C. Escher in 1943. The artwork features a fascinating interplay of perspective and form, depicting a series of reptiles, specifically lizards, that seem to crawl out of a flat surface and into a three-dimensional space. The design exemplifies Escher's skill in creating intriguing visual paradoxes and his exploration of the relationships between two-dimensional and three-dimensional spaces.

The Swallow's Tail is a type of kite and a mathematical shape, often referenced in different contexts. Here are a few explanations of what The Swallow's Tail might refer to: 1. **Mathematics**: In geometry, the Swallow's Tail is a type of differential surface that is shaped like the tail of a swallow. It is described by specific mathematical equations and is known for its unique curvature and properties.

The term "axiom" generally refers to a fundamental principle or starting point that is accepted as true without proof, serving as a foundation for further reasoning or arguments. Axioms are commonly used in mathematics and logic to establish a framework for a theory or system. In mathematics, for example, axioms are the basic assumptions upon which theorems are derived. For instance, in Euclidean geometry, the parallel postulate is an axiom that leads to various geometric propositions.

Blum's axioms are a set of axioms proposed by Manuel Blum, a prominent computer scientist, in the context of the theory of computation and computational complexity. Specifically, these axioms are designed to define the concept of a "computational problem" and provide a formal foundation for discussing the time complexity of algorithms. The axioms cover fundamental aspects that any computational problem must satisfy in order to be considered within the framework of complexity theory.

The Kuratowski closure axioms are a set of foundational properties that define closure operations in a topological space. These axioms provide a formal framework for understanding how closure can be characterized in the context of topology. The closure of a set, denoted as \( \overline{A} \), can be thought of as the smallest closed set containing \( A \), or equivalently, the set of all limit points of \( A \) along with the points in \( A \).