In geometry, an "edge" is defined as a line segment that connects two vertices in a polygon or polyhedron. Edges are one of the fundamental components of geometric shapes, alongside vertices (corners) and faces (surfaces). In two-dimensional shapes like polygons, edges are the straight lines that form the boundary of the shape. For example, a triangle has three edges, while a quadrilateral has four.

In geometry, translation refers to a type of transformation that moves every point of a figure or object a constant distance in a specified direction. This motion is uniform, meaning that all points move the same distance and in the same direction, resulting in a shape that is congruent to the original. Key characteristics of translation include: 1. **Vector Representation**: A translation can be represented using a vector, which indicates the direction and distance of the movement.

In geometry, a "jack" typically refers to a shape that is formed by combining two or more geometric figures. However, the term is more commonly associated with a type of mathematical object known as a "jackknife" or "jack" in the context of certain geometric constructions or games, such as "jackstraws" or "pick-up sticks.

Here's a list of essential formulas in elementary geometry, organized by different geometric figures: ### 1.

A mirror image refers to the reflection of an object or an individual as seen in a mirror. It typically appears reversed or flipped, meaning that the left side of the object appears as the right side in the reflection, and vice versa. This phenomenon can apply to various contexts, including: 1. **Physical Reflection**: When you stand in front of a mirror, your reflection is a mirror image. This reflection shows the same shape and details as you, but inverted laterally.

Tarski's axioms refer to a set of formal axioms proposed by the Polish logician and mathematician Alfred Tarski, particularly in his work on the semantics of formal languages and the theory of truth. Tarski is best known for his semantic definition of truth, which he formalized in the early 20th century.

The **CRC Concise Encyclopedia of Mathematics** is a comprehensive reference work that provides clear and concise explanations of a wide range of mathematical concepts, theories, and terms. Edited by Christopher Thomas A. Brown, the encyclopedia covers topics from various branches of mathematics, including algebra, analysis, geometry, topology, and applied mathematics.

The "Encyclopedia of the History of Arabic Science" is a comprehensive reference work that explores the contributions of Arabic-speaking scholars to the development of science throughout history. This encyclopedia typically covers a wide range of scientific fields, including mathematics, astronomy, medicine, philosophy, and more, highlighting the significant advancements that occurred during the Islamic Golden Age (roughly from the 8th to the 14th centuries).

The timeline of hydrogen technologies spans several centuries, reflecting the evolution of hydrogen production, storage, and applications. Here's an overview highlighting key milestones: ### 18th Century - **1766**: Henry Cavendish discovers hydrogen, calling it "inflammable air." He identifies hydrogen as a distinct substance. ### 19th Century - **1839**: Sir William Grove develops the first fuel cell, the "Grove cell," which converts hydrogen and oxygen into electricity.

Here's a brief timeline of key developments in sustainable energy research from 2020 to the present: ### 2020 - **COVID-19 Impact on Energy**: The pandemic caused a significant drop in energy demand, influencing research on energy systems' resilience and the integration of renewable sources. - **Renewable Energy Growth**: Reports indicated that renewable energy sources surpassed fossil fuels in new power installations globally, with significant advancements in solar and wind technologies.

Alvin M. Weinberg (1915–2006) was an influential American nuclear physicist and a key figure in the development of nuclear energy in the United States. He is best known for his role as the director of the Oak Ridge National Laboratory (ORNL) from 1955 to 1973, where he contributed to various aspects of nuclear research and technology, including the development of nuclear reactors.

The Enrico Fermi Award is a prestigious award presented by the U.S. Department of Energy (DOE) in honor of the Italian-American physicist Enrico Fermi. Established in 1956, the award recognizes individuals for their outstanding contributions to the field of nuclear science and related disciplines, particularly those that have advanced the understanding and application of nuclear energy.

Glenn T. Seaborg was an American chemist and a key figure in the field of nuclear chemistry. He is best known for his role in the discovery of ten elements in the actinide series, including plutonium, americium, and curium. His research significantly advanced the understanding of transuranium elements and their properties.

Liane Russell is known for her pioneering work in the field of genetics. She was a prominent scientist especially recognized for her research on the genetic effects of radiation. One of her significant contributions was her work on the development of techniques for studying the effects of radiation on the genome, particularly in relation to its effects on organisms' reproduction and development. Russell was also instrumental in founding the Oak Ridge National Laboratory's biological research programs and contributed to the understanding of how radiation exposure can lead to genetic mutations.

Herbert York was an American physicist and educator known for his significant contributions to the fields of nuclear physics and arms control. Born on September 24, 1921, and passing away on June 9, 2009, York played a crucial role in the development of the U.S. atomic bomb during World War II as part of the Manhattan Project. After the war, York became involved in nuclear policy, focusing on the implications of nuclear weapons and the need for arms control.

Hyman G. Rickover (1900–1986) was a significant figure in the United States Navy and is often referred to as the "Father of the Nuclear Navy." He was instrumental in developing the U.S. Navy's nuclear submarine program, which revolutionized naval warfare. Rickover was an engineer and an admiral who played a key role in the design and construction of the first nuclear-powered submarines, starting with the USS Nautilus, which was launched in 1954.

Manson Benedict is not a widely recognized term in mainstream topics, but it may refer to the Benedict's formula or the Manson criteria used in different fields. It’s possible that you could be referring to: 1. **Mannheim Criteria** - Related to hemodynamic stability or other medical criteria. 2. **Benedict's Formula** - A method used in nutrition and metabolic studies to estimate an individual's basal metabolic rate (BMR).

Martin Kamen was an American chemist known for his significant contributions to the fields of nuclear chemistry and biochemistry. He is perhaps best known for his role in the discovery of carbon-14 in 1940, along with his colleague Sam Ruben. This isotope of carbon became a crucial tool for radiocarbon dating, which is widely used in archaeology and geology to date ancient organic materials.

Michael E. Phelps is an American nuclear scientist and a prominent figure in the field of medical imaging. He is best known for his pioneering work in positron emission tomography (PET), a technique that allows for the visualization and measurement of metabolic processes in the body. Phelps developed the first clinical PET scanner and has made significant contributions to the advancement of imaging technologies in medicine, leading to improved diagnosis and treatment of various diseases, particularly cancer.

Chaotropic activity refers to the ability of certain substances to disrupt the structure of water and other solvents, leading to an increase in the solubility of molecules that are normally poorly soluble. The term "chaotropic agent" typically describes chemical compounds that decrease the order of water molecules, effectively increasing the disorder (or chaos) in the system. This can affect the stability of biological molecules, such as proteins and nucleic acids, by denaturing them or altering their conformations.