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Systems Encyclopedia Entry 1778683699

The **Systems Encyclopedia Entry 1778683699** refers to a comprehensive and authoritative article about various systems, including their definitions, types, and applications, providing a valuable resource for understanding complex systems and their interconnectedness.

Scientists Encyclopedia Entry 1778070967

The **Scientists Encyclopedia Entry 1778070967** is a comprehensive online database that provides detailed information about the lives and achievements of renowned scientists throughout history, offering a valuable resource for researchers, students, and science enthusiasts alike.

Systems Encyclopedia Entry 1778913306

A system is a set of interrelated and organized components that work together to achieve a common goal or objective, often exhibiting complex behavior and emergent properties.

Applications Encyclopedia Entry 1780240205

The **Applications Encyclopedia Entry 1780240205** is a comprehensive digital repository that showcases the diverse and innovative applications of mathematical concepts and techniques in various fields, highlighting their practical significance and real-world impact.

Applications Encyclopedia Entry 1779256625

Applications refer to the practical uses and implementations of mathematical concepts, theories, and models in various fields, including science, engineering, economics, and social sciences.

Landmarks Encyclopedia Entry 1778177768

The **Eiffel Tower**, a monumental iron lattice tower, is an iconic symbol of Paris, France, and one of the most recognizable landmarks in the world, attracting millions of visitors each year.

Scientists Encyclopedia Entry 1780399806

Theorems Encyclopedia Entry 1779107344

A theorem is a mathematical statement that has been rigorously proven to be true, often serving as a fundamental building block for further mathematical discoveries and applications.

Computing Encyclopedia Entry 1780322302

** Computing refers to the use of computers to process, store, and communicate information, encompassing a wide range of fields, including computer science, engineering, and mathematics. **CONTENT:** ### Overview Computing is a broad field that involves the design, development, and application of computer systems and algorithms to solve real-world problems. Computing encompasses a wide range of disciplines, including computer science, engineering, mathematics, and information technology. At its core, computing involves the use of computers to process, store, and communicate information, which has revolutionized the way we live, work, and interact with one another. Computing has become an integral part of modern life, with applications in fields such as healthcare, finance, education, and entertainment. From simple calculators to complex supercomputers, computing has evolved significantly over the years, driven by advances in technology, software, and hardware. Today, computing is a global industry that employs millions of people and has a significant impact on the economy and society. ### History/Background The history of computing dates back to the early 19th century, when Charles Babbage designed the first mechanical computer, the Difference Engine. However, it was not until the mid-20th century that computing began to take shape as a distinct field. The development of the first electronic computers, such as ENIAC (1946) and UNIVAC (1951), marked the beginning of the computing era. The 1960s saw the introduction of the first commercial computers, such as the IBM System/360, which became a standard for the industry. The development of programming languages, such as COBOL (1959) and FORTRAN (1957), made it easier for people to interact with computers. The 1970s and 1980s saw the rise of personal computers, such as the Apple II (1977) and IBM PC (1981), which democratized access to computing and paved the way for the modern computing landscape. ### Key Information **Key Milestones:** - **1946:** ENIAC (Electronic Numerical Integrator and Computer) is developed, marking the beginning of the computing era. - **1951:** UNIVAC (Universal Automatic Computer) is introduced, the first commercially available computer. - **1957:** FORTRAN (FORmula TRANslating system) is developed, a programming language for scientific computing. - **1959:** COBOL (Common Business Oriented Language) is developed, a programming language for business applications. - **1977:** Apple II is introduced, one of the first successful personal computers. - **1981:** IBM PC is introduced, a widely adopted personal computer. **Key Concepts:** - **Algorithms:** A set of instructions that a computer follows to solve a problem or perform a task. - **Software:** Programs and operating systems that run on computers. - **Hardware:** The physical components of a computer, such as the CPU, memory, and storage. ### Significance Computing has had a profound impact on modern society, transforming the way we live, work, and interact with one another. Computing has enabled: - **Global Connectivity:** The internet and social media have connected people across the globe, facilitating communication and collaboration. - **Economic Growth:** Computing has enabled the development of new industries, such as e-commerce and fintech, and has increased productivity and efficiency in existing industries. - **Scientific Advancements:** Computing has enabled significant advances in fields such as medicine, astronomy, and climate science. INFOBOX: - **Name:** Computing - **Type:** Field of study - **Date:** 1946 (ENIAC) - **Location:** Global - **Known For:** Revolutionizing the way we live, work, and interact with one another TAGS: computer science, engineering, mathematics, information technology, algorithms, software, hardware, global connectivity, economic growth, scientific advancements

Mathematicians Encyclopedia Entry 1778641925

The Mathematicians Encyclopedia Entry 1778641925 is a comprehensive collection of information about the lives, contributions, and achievements of renowned mathematicians throughout history.

Figures Encyclopedia Entry 1778717344

** Figures are a type of mathematical concept that represents a quantity or magnitude, often used in various fields such as science, engineering, and economics. **CONTENT:** ## Overview Figures are a fundamental concept in mathematics, used to represent a quantity or magnitude. They can be expressed as numbers, symbols, or even geometric shapes. In various fields, figures are used to describe and analyze complex phenomena, making them an essential tool for scientists, engineers, and economists. The concept of figures has evolved over time, with different cultures and civilizations contributing to its development. The term "figure" can refer to various mathematical concepts, including numbers, fractions, decimals, and geometric shapes. In everyday language, figures are often used to describe quantities, such as the number of people, the amount of money, or the size of an object. However, in mathematics, figures have a more precise meaning, referring to the representation of a quantity or magnitude. ## History/Background The concept of figures dates back to ancient civilizations, where people used various methods to represent quantities. The Babylonians, for example, used a sexagesimal (base-60) system to represent numbers, which is still used today for measuring time and angles. The ancient Greeks made significant contributions to the development of mathematics, introducing concepts such as fractions and decimals. The Indian mathematician Aryabhata (476 CE) is credited with developing the concept of zero, which revolutionized the representation of figures. In the Middle Ages, mathematicians such as Fibonacci (1202 CE) and Luca Pacioli (1494 CE) made significant contributions to the development of arithmetic and algebra. The invention of the printing press (1450 CE) facilitated the dissemination of mathematical knowledge, leading to a rapid growth in mathematical discoveries. In the 17th and 18th centuries, mathematicians such as Isaac Newton (1687 CE) and Leonhard Euler (1740 CE) developed calculus, which enabled the representation of complex phenomena using figures. ## Key Information Figures are used in various fields, including: * **Science**: Figures are used to describe and analyze complex phenomena, such as the motion of objects, the behavior of particles, and the properties of materials. * **Engineering**: Figures are used to design and optimize systems, such as bridges, buildings, and machines. * **Economics**: Figures are used to analyze and predict economic trends, such as inflation, unemployment, and GDP. * **Statistics**: Figures are used to describe and analyze data, such as population growth, crime rates, and election results. Some key properties of figures include: * **Magnitude**: Figures can be expressed as numbers, symbols, or geometric shapes. * **Units**: Figures can be expressed in various units, such as meters, kilograms, or dollars. * **Precision**: Figures can be expressed with varying degrees of precision, such as decimal places or significant figures. ## Significance Figures are essential in various fields, enabling scientists, engineers, and economists to analyze and understand complex phenomena. The development of figures has facilitated significant advances in science, technology, and economics, leading to improvements in quality of life and economic growth. The concept of figures continues to evolve, with new mathematical discoveries and technological innovations enabling more precise and accurate representations of quantities. **INFOBOX:** - **Name:** Figures - **Type:** Mathematical concept - **Date:** Ancient civilizations (Babylonians, Greeks, Indians) - **Location:** Global - **Known For:** Representing quantities and magnitudes **TAGS:** mathematics, numbers, fractions, decimals, geometry, science, engineering, economics, statistics, precision, magnitude, units.

Applications Encyclopedia Entry 1776481624

Applications refer to the practical uses and implementations of mathematical concepts, theories, and models in various fields, including science, engineering, economics, and social sciences.

Theorems Encyclopedia Entry 1778617459

** Theorems are statements in mathematics that have been proven to be true, often with significant implications for various fields of study. **CONTENT:** ### Overview A **theorem** is a statement in mathematics that has been rigorously proven to be true. Theorems are often considered the foundation of mathematics, as they provide a framework for understanding and describing the world around us. Theorems can be found in various branches of mathematics, including algebra, geometry, analysis, and number theory. They are typically stated in a precise and concise manner, using mathematical notation and terminology. Theorems are not just abstract concepts; they have real-world applications and implications. For example, the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides, has been used in architecture, engineering, and physics for centuries. Similarly, the Fundamental Theorem of Calculus, which relates the derivative of a function to its integral, has been used in fields such as economics, biology, and computer science. Theorems are often developed through a process of mathematical inquiry, which involves formulating conjectures, testing hypotheses, and proving theorems. This process requires a deep understanding of mathematical concepts and techniques, as well as the ability to communicate complex ideas clearly and concisely. ### History/Background The concept of theorems dates back to ancient civilizations, where mathematicians such as Euclid and Archimedes developed and proved mathematical statements. However, it was not until the 19th century that the modern concept of theorems as we know it today began to take shape. In the 19th century, mathematicians such as David Hilbert and Henri Poincaré developed the concept of axiomatic systems, which provided a foundation for the development of theorems. Axiomatic systems are sets of axioms, or self-evident truths, that are used to derive theorems. This approach allowed mathematicians to develop theorems in a more systematic and rigorous manner. ### Key Information Some of the most famous theorems in mathematics include: * **Pythagorean theorem**: a² + b² = c², where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse. * **Fundamental Theorem of Calculus**: ∫f(x)dx = F(x) + C, where F(x) is the antiderivative of f(x), and C is a constant. * **Fermat's Last Theorem**: a^n + b^n ≠ c^n for n > 2, where a, b, and c are integers. * **Euler's Identity**: e^(iπ) + 1 = 0, where e is the base of the natural logarithm, and i is the imaginary unit. These theorems have had a profound impact on mathematics and have been used to develop many other theorems and mathematical concepts. ### Significance Theorems are significant because they provide a foundation for understanding and describing the world around us. They have been used to develop many other mathematical concepts and have had a profound impact on various fields of study, including physics, engineering, economics, and computer science. Theorems also have a profound impact on the development of mathematics itself. They provide a framework for understanding and describing mathematical concepts, and they have been used to develop many other theorems and mathematical concepts. **INFOBOX:** - **Name:** Theorems - **Type:** Mathematical statements - **Date:** Ancient civilizations to present day - **Location:** Global - **Known For:** Providing a foundation for understanding and describing the world around us **TAGS:** Theorems, mathematics, axiomatic systems, proof, rigor, mathematical notation, terminology, Pythagorean theorem, Fundamental Theorem of Calculus, Fermat's Last Theorem, Euler's Identity, mathematical concepts, physics, engineering, economics, computer science.

Figures Encyclopedia Entry 1779003006

** Figures are a type of mathematical concept used to represent the magnitude of a quantity, often used in geometry and algebra to describe shapes and relationships. **CONTENT:** ### Overview In mathematics, figures are a fundamental concept used to describe and analyze geometric shapes, relationships, and quantities. The term "figure" can refer to a wide range of mathematical objects, including points, lines, planes, and solids. Figures are essential in various branches of mathematics, such as geometry, algebra, and calculus, and have numerous applications in science, engineering, and technology. Understanding figures is crucial for solving problems, making predictions, and modeling real-world phenomena. The concept of figures dates back to ancient civilizations, where mathematicians and philosophers used geometric shapes to describe the world around them. The ancient Greeks, in particular, made significant contributions to the development of geometry, laying the foundation for modern mathematical concepts. Over time, the study of figures has evolved to incorporate new mathematical tools and techniques, enabling mathematicians to tackle increasingly complex problems. In modern mathematics, figures are used to describe a wide range of concepts, from simple geometric shapes to complex fractals and topological spaces. The study of figures has far-reaching implications, influencing fields such as physics, engineering, computer science, and economics. ### History/Background The concept of figures has its roots in ancient civilizations, where mathematicians and philosophers used geometric shapes to describe the world around them. The ancient Greeks made significant contributions to the development of geometry, with mathematicians such as Euclid and Archimedes laying the foundation for modern mathematical concepts. The Greek concept of "geometria" referred to the study of shapes and sizes, which laid the groundwork for the development of modern geometry. During the Middle Ages, mathematicians such as Fibonacci and Al-Khwarizmi made significant contributions to the development of algebra and geometry. The Renaissance saw a resurgence of interest in classical Greek mathematics, with mathematicians such as Leonardo da Vinci and Galileo Galilei making significant contributions to the field. In the 19th century, mathematicians such as Carl Friedrich Gauss and Bernhard Riemann developed new mathematical tools and techniques, enabling the study of complex figures and spaces. The 20th century saw the development of new mathematical fields, such as topology and fractal geometry, which have had a profound impact on our understanding of figures. ### Key Information * **Definition:** A figure is a mathematical concept used to represent the magnitude of a quantity, often used in geometry and algebra to describe shapes and relationships. * **Types:** Figures can be classified into various types, including points, lines, planes, and solids. * **Properties:** Figures have various properties, including length, area, and volume, which can be used to describe and analyze geometric shapes. * **Applications:** Figures have numerous applications in science, engineering, and technology, including physics, engineering, computer science, and economics. * **Mathematical tools:** Figures are used in conjunction with various mathematical tools, including geometry, algebra, and calculus. ### Significance The study of figures has far-reaching implications, influencing fields such as physics, engineering, computer science, and economics. Understanding figures is crucial for solving problems, making predictions, and modeling real-world phenomena. The development of new mathematical tools and techniques has enabled mathematicians to tackle increasingly complex problems, leading to breakthroughs in fields such as medicine, finance, and climate science. In conclusion, figures are a fundamental concept in mathematics, used to describe and analyze geometric shapes, relationships, and quantities. The study of figures has a rich history, dating back to ancient civilizations, and has far-reaching implications for various fields of study. **INFOBOX:** - **Name:** Figures - **Type:** Mathematical concept - **Date:** Ancient civilizations (circa 500 BCE) - **Location:** Global - **Known For:** Representing the magnitude of a quantity in geometry and algebra **TAGS:** geometry, algebra, calculus, mathematics, science, engineering, technology, physics, computer science, economics.

Theorems Encyclopedia Entry 1777773784

The **Theorems Encyclopedia Entry 1777773784** is a comprehensive collection of mathematical theorems that provides a detailed understanding of various mathematical concepts and their applications.

Figures Encyclopedia Entry 1779164524

** Figures are a type of mathematical concept used in geometry to describe the shape and size of an object or a set of points in space. **CONTENT:** ### Overview In mathematics, a figure is a geometric concept that refers to a set of points, lines, and shapes that are connected or related in some way. Figures can be two-dimensional (2D) or three-dimensional (3D), and they can be used to describe a wide range of objects and concepts in mathematics, science, and engineering. From simple shapes like triangles and circles to complex structures like buildings and bridges, figures play a crucial role in understanding the world around us. The study of figures is a fundamental aspect of geometry, which is the branch of mathematics that deals with the properties and relationships of points, lines, and shapes. Geometers use figures to describe and analyze the properties of objects, such as their size, shape, and position in space. By studying figures, mathematicians and scientists can gain insights into the underlying structure and behavior of complex systems, from the movement of celestial bodies to the behavior of subatomic particles. ### History/Background The concept of figures dates back to ancient civilizations, where mathematicians and philosophers used geometric shapes to describe the world around them. The ancient Greeks, in particular, made significant contributions to the development of geometry, with mathematicians like Euclid and Archimedes laying the foundations for the study of figures. In the Middle Ages, mathematicians like Fibonacci and Al-Khwarizmi continued to develop the field of geometry, introducing new concepts and techniques for working with figures. In the modern era, the study of figures has become increasingly sophisticated, with the development of new mathematical tools and techniques. The discovery of non-Euclidean geometries in the 19th century, for example, revolutionized the field of geometry, allowing mathematicians to describe and analyze figures in new and innovative ways. Today, the study of figures is a vibrant and dynamic field, with applications in a wide range of areas, from physics and engineering to computer science and data analysis. ### Key Information Some of the key concepts and techniques associated with figures include: * **Points**: A point is a location in space, represented by a set of coordinates (x, y, z). * **Lines**: A line is a set of points that extend infinitely in two directions, represented by a set of equations (ax + by + cz = d). * **Planes**: A plane is a flat surface that extends infinitely in all directions, represented by a set of equations (ax + by + cz = d). * **Polygons**: A polygon is a closed shape with at least three sides, represented by a set of vertices and edges. * **Circles**: A circle is a closed shape with a single center and a constant radius, represented by a set of points on a plane. Figures can be used to describe a wide range of objects and concepts, from simple shapes like triangles and circles to complex structures like buildings and bridges. In addition, figures can be used to analyze and understand the properties of objects, such as their size, shape, and position in space. ### Significance The study of figures is significant because it provides a fundamental understanding of the world around us. By studying figures, mathematicians and scientists can gain insights into the underlying structure and behavior of complex systems, from the movement of celestial bodies to the behavior of subatomic particles. In addition, the study of figures has numerous practical applications, from engineering and architecture to computer science and data analysis. **INFOBOX:** - **Name:** Figures - **Type:** Mathematical concept - **Date:** Ancient civilizations (circa 3000 BCE) - **Location:** Global - **Known For:** Describing and analyzing the properties of objects in space **TAGS:** geometry, mathematics, figures, points, lines, planes, polygons, circles, shapes, size, position, space, geometry, mathematics, science, engineering, computer science, data analysis

Applications Encyclopedia Entry 1776635165

Applications refer to the practical uses and implementations of mathematical concepts, theories, and models in various fields, including science, engineering, economics, and finance.

Theorems Encyclopedia Entry 1778646498

** A theorem is a mathematical statement that has been rigorously proven to be true, often serving as a fundamental building block for further mathematical discoveries. **CONTENT:** ### Overview A theorem is a fundamental concept in mathematics, representing a statement that has been thoroughly proven to be true. It is often a culmination of various mathematical theories, principles, and axioms, and serves as a cornerstone for further mathematical exploration and discovery. Theorems can be found in various branches of mathematics, including algebra, geometry, calculus, and number theory. They are typically expressed in a precise and concise manner, using mathematical notation and language. Theorems are often developed through a process of mathematical inquiry, where mathematicians use logical reasoning, mathematical proofs, and empirical evidence to establish their validity. The process of proving a theorem involves demonstrating its truth through a series of logical steps, using established mathematical principles and axioms. This process can be iterative, with the development of new theorems often leading to the refinement or revision of existing ones. Theorems have far-reaching implications, influencing not only mathematics but also other fields such as physics, engineering, computer science, and economics. They provide a foundation for mathematical modeling, problem-solving, and decision-making, enabling mathematicians and scientists to make predictions, analyze data, and optimize systems. ### History/Background The concept of theorems dates back to ancient civilizations, where mathematicians such as Euclid and Archimedes developed and proved various mathematical statements. However, it was not until the 19th century that the modern concept of theorems began to take shape. Mathematicians such as David Hilbert and Henri Poincaré developed the idea of axiomatic systems, which provided a rigorous framework for mathematical proofs and theorems. The 20th century saw a significant expansion of the concept of theorems, with the development of new mathematical disciplines such as topology, algebraic geometry, and number theory. Mathematicians such as Andrew Wiles, Grigori Perelman, and Maryam Mirzakhani made groundbreaking contributions to these fields, establishing new theorems and solving long-standing problems. ### Key Information * **Types of Theorems:** There are various types of theorems, including: + **Theorem:** A general statement that has been proven to be true. + **Corollary:** A statement that follows directly from a theorem. + **Lemma:** A statement that is used to prove a theorem. + **Conjecture:** A statement that has not been proven to be true, but is believed to be so. * **Mathematical Proofs:** The process of proving a theorem involves demonstrating its truth through a series of logical steps, using established mathematical principles and axioms. * **Mathematical Notation:** Theorems are often expressed in a precise and concise manner, using mathematical notation and language. * **Applications:** Theorems have far-reaching implications, influencing not only mathematics but also other fields such as physics, engineering, computer science, and economics. ### Significance Theorems are a fundamental component of mathematics, providing a foundation for mathematical modeling, problem-solving, and decision-making. They have far-reaching implications, influencing not only mathematics but also other fields such as physics, engineering, computer science, and economics. Theorems have also played a significant role in shaping our understanding of the world, enabling mathematicians and scientists to make predictions, analyze data, and optimize systems. The development of new theorems has also led to significant advances in technology, medicine, and other fields. For example, the development of the **Four Color Theorem** by Kenneth Appel and Wolfgang Haken in 1976 led to significant advances in computer graphics and cartography. Similarly, the development of the **Poincaré Conjecture** by Grigori Perelman in 2003 led to significant advances in topology and geometry. **INFOBOX:** - Name: Theorems - Type: Mathematical concept - Date: Ancient civilizations (Euclid and Archimedes) - Location: Global - Known For: Fundamental building blocks of mathematics **TAGS:** mathematics, theorems, proofs, mathematical notation, applications, physics, engineering, computer science, economics.

Applications Encyclopedia Entry 1779437105

Applications refer to the practical uses and implementations of mathematical concepts, theories, and models in various fields, including science, engineering, economics, and social sciences.

Artists Encyclopedia Entry 1778235124

** This encyclopedia entry is dedicated to the life and work of renowned artist, **Leonardo da Vinci** (1452-1519), a true Renaissance man whose contributions to art, science, engineering, mathematics, and anatomy continue to inspire and influence artists, scientists, and thinkers to this day. ## Overview Leonardo da Vinci was a polymath, an Italian artist, inventor, engineer, and scientist who is widely considered one of the greatest painters of all time. Born in Vinci, Italy, on April 15, 1452, da Vinci was the illegitimate son of a notary and a peasant woman. Despite his humble beginnings, he was apprenticed to the artist Andrea del Verrocchio in Florence at the age of 14, where he refined his painting, sculpture, and engineering skills. Da Vinci's artistic style was characterized by his use of sfumato, a technique that creates a soft, hazy effect by layering thin glazes of paint over a base coat. His innovative approach to art, combined with his boundless curiosity and inventive spirit, made him a true master of his craft. Da Vinci's artistic output was incredibly diverse, spanning painting, sculpture, architecture, engineering, and anatomy. He is perhaps best known for his iconic works, such as the **Mona Lisa** (1503-1506) and **The Last Supper** (1495-1498), which continue to captivate art lovers and historians alike. However, his contributions to science and engineering are equally impressive, as evidenced by his designs for flying machines, armored vehicles, and submarines, which were well ahead of their time. ## History/Background Da Vinci's artistic career spanned over four decades, during which he worked in various cities, including Florence, Milan, and Rome. He was a true Renaissance man, and his interests and talents knew no bounds. In addition to his artistic pursuits, da Vinci was a prolific inventor and engineer, designing innovative machines and devices that were often centuries ahead of their time. His fascination with anatomy led him to make detailed drawings of the human body, which were used by artists and scientists for centuries. Da Vinci's most famous patron was **Ludovico Sforza**, the Duke of Milan, who commissioned him to paint **The Last Supper**. Da Vinci's work on this project was interrupted by his involvement in the wars between the French and the Sforza family, which led to his eventual departure from Milan. He spent the final years of his life in France, where he was welcomed by King Francis I, who recognized his genius and provided him with a comfortable living. ## Key Information - **Artistic Style:** Da Vinci's artistic style was characterized by his use of sfumato, a technique that creates a soft, hazy effect by layering thin glazes of paint over a base coat. - **Notable Works:** **Mona Lisa** (1503-1506), **The Last Supper** (1495-1498), **Vitruvian Man** (1490) - **Inventions:** Flying machines, armored vehicles, submarines, mechanical lions, and other innovative devices - **Anatomical Studies:** Da Vinci made detailed drawings of the human body, which were used by artists and scientists for centuries - **Patronage:** Da Vinci was patronized by **Ludovico Sforza**, the Duke of Milan, and **King Francis I** of France ## Significance Da Vinci's impact on art, science, and engineering cannot be overstated. His innovative approach to art, combined with his boundless curiosity and inventive spirit, made him a true master of his craft. His contributions to anatomy and engineering have had a lasting impact on the development of these fields, and his artistic style continues to inspire artists and art lovers to this day. As a true Renaissance man, da Vinci's legacy extends far beyond his artistic output, representing the very best of human creativity, innovation, and curiosity. INFOBOX: - Name: Leonardo da Vinci - Type: Artist, Inventor, Engineer, Scientist - Date: 1452-1519 - Location: Vinci, Italy - Known For: **Mona Lisa**, **The Last Supper**, innovative artistic style, and contributions to science and engineering TAGS: Renaissance art, Leonardo da Vinci, Mona Lisa, The Last Supper, sfumato, Vitruvian Man, anatomy, engineering, science, innovation, Renaissance man.