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Coin Rotation Paradox
The coin rotation paradox is the veridical paradox, counter-intuitive mathematical fact that, when one coin is rolled without slipping around the rim of another coin of equal size, the moving coin completes not one but two full rotations after going all the way around the stationary coin, when viewed from an external reference frame. The problem can be further generalized to coins of different radii. Description Start with two identical coins touching each other on a table, with their "head" sides displayed and parallel. Keeping coin A stationary, rotate coin B around A, keeping a point of contact with no slippage. As coin B reaches the opposite side, the two heads will again be parallel; B has made one revolution. Continuing to move B brings it back to the starting position and completes a second revolution. Paradoxically, coin B appears to have rolled a distance equal to twice its circumference. In reality, as the circumferences of both coins are equal, by definition coin B h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Coin Reverse Rotation Paradox
A coin is a small object, usually round and flat, used primarily as a medium of exchange or legal tender. They are standardized in weight, and produced in large quantities at a mint in order to facilitate trade. They are most often issued by a government. Coins often have images, numerals, or text on them. The faces of coins or medals are sometimes called the ''obverse'' and the ''reverse'', referring to the front and back sides, respectively. The obverse of a coin is commonly called ''heads'', because it often depicts the head of a prominent person, and the reverse is known as ''tails''. The first metal coins – invented in the ancient Greek world and disseminated during the Hellenistic period – were precious metal–based, and were invented in order to simplify and regularize the task of measuring and weighing bullion (bulk metal) carried around for the purpose of transactions. They carried their value within the coins themselves, but the stampings also induced manipulati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sidereal Day
Sidereal time ("sidereal" pronounced ) is a system of timekeeping used especially by astronomers. Using sidereal time and the celestial coordinate system, it is easy to locate the positions of celestial objects in the night sky. Sidereal time is a "time scale that is based on Earth's rate of rotation measured relative to the fixed stars". A sidereal day (also known as the sidereal rotation period) represents the time for one rotation about the planet axis relative to the stars. Viewed from the same location, a star seen at one position in the sky will be seen at the same position on another night at the same time of day (or night), if the day is defined as a sidereal day. This is similar to how the time kept by a sundial (Solar time) can be used to find the location of the Sun. Just as the Sun and Moon appear to rise in the east and set in the west due to the rotation of Earth, so do the stars. Both solar time and sidereal time make use of the regularity of Earth's rot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Paradoxes
Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself. There are many areas of mathematics, which include number theory (the study of numbers), algebra (the study of formulas and related structures), geometry (the study of shapes and spaces that contain them), analysis (the study of continuous changes), and set theory (presently used as a foundation for all mathematics). Mathematics involves the description and manipulation of abstract objects that consist of either abstractions from nature orin modern mathematicspurely abstract entities that are stipulated to have certain properties, called axioms. Mathematics uses pure reason to prove properties of objects, a ''proof'' consisting of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Veritasium
Derek Alexander Muller (born 9 November 1982) is a Science communication, science communicator and media personality, best known for his YouTube channel Veritasium, which has over 17.8 million subscribers and 3.3 billion views as of April 2025. He currently lives in Los Angeles. Early life and education Muller was born to South African parents in Traralgon, Victoria (Australia), Victoria, Australia. His family moved to Vancouver, British Columbia, Canada, when he was 18 months old. In 2000, Muller graduated from West Vancouver Secondary School. In 2004, Muller graduated from Queen's University at Kingston, Queen's University in Kingston, Ontario, with a Bachelor of Applied Science in Engineering Physics. Muller moved to Australia to study film-making; however, he instead enrolled for a Ph.D. in physics education research from the University of Sydney, which he completed in 2008 with a thesis: ''Designing Effective Multimedia for Physics Education''. Career Muller has been lis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
YouTube
YouTube is an American social media and online video sharing platform owned by Google. YouTube was founded on February 14, 2005, by Steve Chen, Chad Hurley, and Jawed Karim who were three former employees of PayPal. Headquartered in San Bruno, California, it is the second-most-visited website in the world, after Google Search. In January 2024, YouTube had more than 2.7billion monthly active users, who collectively watched more than one billion hours of videos every day. , videos were being uploaded to the platform at a rate of more than 500 hours of content per minute, and , there were approximately 14.8billion videos in total. On November 13, 2006, YouTube was purchased by Google for $1.65 billion (equivalent to $ billion in ). Google expanded YouTube's business model of generating revenue from advertisements alone, to offering paid content such as movies and exclusive content produced by and for YouTube. It also offers YouTube Premium, a paid subs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quora
Quora is an American social question-and-answer website and online knowledge market headquartered in Mountain View, California. It was founded on June 25, 2009, and made available to the public on June 21, 2010. Users can post questions, answer questions, and comment on answers that have been submitted by other users. As of 2020, the website was visited by 300million users a month. History Founding and naming Quora was co-founded by former Facebook employees Adam D'Angelo and Charlie Cheever in June 2009. In an answer to the question, "How did Adam D'Angelo and Charlie Cheever come up with the name Quora?" Cheever wrote: We spent a few hours brainstorming and writing down all the ideas that we could think of. After consulting with friends and eliminating ones we didn't love, we narrowed it down to 5 or 6 finalists, and eventually settled on Quora. The closest competition that he nameQuora had was Quiver. 2010–2013: Early growth In March 2010, Quora, Inc. was valu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aristotle's Wheel Paradox
Aristotle's wheel paradox is a paradox or problem appearing in the Pseudo-Aristotle, pseudo-Aristotelian Ancient Greece, Greek work ''Mechanics (Aristotle), Mechanica''. It states as follows: A wheel is depicted in two-dimensional space as two circles. Its larger, outer circle is tangential to a horizontal surface (e.g. a road that it rolls on), while the smaller, inner one has the same center and is rigidly affixed to the larger. (The smaller circle could be the bead of a tire, the rim it is mounted upon, or the axle.) Assuming the larger circle rolls without slipping (or skidding) for one full revolution, the distances moved by both circles' circumferences are the same. The distance travelled by the larger circle is equal to its circumference, but for the smaller it is greater than its circumference, thereby creating a paradox. The paradox is not limited to wheels: other things depicted in two dimensions display the same behavior such as a roll of tape, or a typical round bottle ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
G2 (mathematics)
In mathematics, G2 is three simple Lie groups (a complex form, a compact real form and a split real form), their Lie algebras \mathfrak_2, as well as some algebraic groups. They are the smallest of the five exceptional simple Lie groups. G2 has rank 2 and dimension 14. It has two fundamental representations, with dimension 7 and 14. The compact form of G2 can be described as the automorphism group of the Octonion, octonion algebra or, equivalently, as the subgroup of SO(7) that preserves any chosen particular vector in its 8-dimensional Real representation, real spinor Group representation, representation (a spin representation). History The Lie algebra \mathfrak_2, being the smallest exceptional simple Lie algebra, was the first of these to be discovered in the attempt to classify simple Lie algebras. On May 23, 1887, Wilhelm Killing wrote a letter to Friedrich Engel (mathematician), Friedrich Engel saying that he had found a 14-dimensional simple Lie algebra, which we now ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lie Group
In mathematics, a Lie group (pronounced ) is a group (mathematics), group that is also a differentiable manifold, such that group multiplication and taking inverses are both differentiable. A manifold is a space that locally resembles Euclidean space, whereas groups define the abstract concept of a binary operation along with the additional properties it must have to be thought of as a "transformation" in the abstract sense, for instance multiplication and the taking of inverses (to allow division), or equivalently, the concept of addition and subtraction. Combining these two ideas, one obtains a continuous group where multiplying points and their inverses is continuous. If the multiplication and taking of inverses are smoothness, smooth (differentiable) as well, one obtains a Lie group. Lie groups provide a natural model for the concept of continuous symmetry, a celebrated example of which is the circle group. Rotating a circle is an example of a continuous symmetry. For an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theory
In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also cen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Solar Day
A synodic day (or synodic rotation period or solar day) is the period for a celestial object to rotate once in relation to the star it is orbiting, and is the basis of solar time. The synodic day is distinguished from the sidereal day, which is one complete rotation in relation to distant stars and is the basis of sidereal time. In the case of a tidally locked planet, the same side always faces its parent star, and its synodic day is infinite. Its sidereal day, however, is equal to its orbital period. Earth Earth's synodic day is the time it takes for the Sun to pass over the same meridian (a line of longitude) on consecutive days, whereas a sidereal day is the time it takes for a given distant star to pass over a meridian on consecutive days. For example, in the Northern Hemisphere, a synodic day could be measured as the time taken for the Sun to move from exactly true south (i.e. its highest declination) on one day to exactly south again on the next day (or exactly true ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
