Diophantus of Alexandria (Ancient Greek: Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died aged 84, probably sometime between AD 285 and 299), sometimes called "the father of algebra", was an AlexandrianGreek mathematician and the author of a series of books called Arithmetica, many of which are now lost. These texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' Arithmetica,Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations ("Diophantine geometry") and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positiverational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation.
Diophantus is a lunarimpact crater that lies in the southwestern part of the Mare Imbrium. It forms a pair with the larger crater Delisle to the north. Diophantus has a wide inner wall and a low central rise. To the north of Diophantus is the sinuous rille designated Rima Diophantus, named after the crater. There is a tiny craterlet near the exterior of the southwest wall.
Rima Diophantus
This cleft follows a generally east–west path across the Mare Imbrium. It is centered at selenographic coordinates 31.0° N, 32.0° W, and has a maximum diameter of 150km. Several tiny craters near this rille have been assigned names by the IAU. These are listed in the table below.
The crater Samir has bright rays that extend for over 70km.
Satellite craters
By convention these features are identified on lunar maps by placing the letter on the side of the crater midpoint that is closest to Diophantus.
The following craters have been renamed by the IAU.
Diophantus (Greek:Διόφαντος), son of Asclepiodorus, of Sinope, was a general in the service of Mithridates VI of Pontus. Diophantus was active in Mithridates' campaigns in the Bosporan Kingdom and elsewhere around the Black Sea, although their chronology is disputed. An inscription found during the excavations in Chersonesos glorifies Diophantus as "the first foreign invader to conquer the Scythians".
During his first Crimean expedition, he relieved the siege of Chersonesos by the Scythian king Palacus and subdued his allies, the Tauri. He finished this campaign at Scythian Neapolis. During the second campaign, Diophantus checked another invasion of the Scythians, who had joined their forces with the Rhoxolanoi under Tasius. At one point during these campaigns he established a stronghold at Eupatorium on the eastern shore of the Crimea.
Around 107 BC, Mithridates dispatched Diophantes to Panticapaeum with the task of persuading the Bosporan king Paerisades V to cede his kingdom to Mithridates. While he was in the city, the Scythians, led by a certain Saumacus, revolted and killed Paerisades, while Diophantes barely managed to escape to Chersonesos. Back in Pontus, Diophantes rallied his forces and sailed to Crimea with a large fleet. The Scythian uprising was put down and the Bosporan kingdom was reduced to a dependency of Pontus.
Diophantus of Alexandria is an important figure in the history of math. Watch to find out more!
For further reference check out:
https://en.wikipedia.org/wiki/Diophantus
http://www-history.mcs.st-and.ac.uk/Biographies/Diophantus.html
https://www.famousscientists.org/diophantus/
https://en.wikipedia.org/wiki/Metrodorus_(grammarian)
https://www.famousmathematicians.net/diophantus/
https://en.wikipedia.org/wiki/History_of_mathematical_notation
https://www.metmuseum.org/toah/hd/roem/hd_roem.htm
published: 05 Mar 2019
Diophantus part 1: Introduction: his life, work, influence
Introduces what we know about Diophantus' life and the structure of his main work (the 'Arithmetica'), and outline the partial survival of his work and the history of its influence, including on Fermat's Last Theorem.
published: 29 Mar 2021
Diophantus and Syncopated Notation
Introduction to the syncopated notation of Diophantus.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
published: 21 May 2020
Diophantus's Sum of Squares Identity I (visual proof)
This is a short, animated visual proof of Diophantus's sum of squares identity (also sometimes called the Brahmagupta–Fibonacci identity) using "Garfield's trapezoid" and scaling of right triangles.
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
To see a related proof of the Cauchy-Schwarz inequality, check out:
https://youtu.be/OWR6QCPYjqI
This animation is based on a visual proof by Roger Nelsen from the April 2017 issue of Mathematics Magazine (https://doi.org/10.4169/math.mag.90.2.134 - page 134).
#math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #diophantus #algebraicidentity #mathshorts #mathvid...
published: 30 Jun 2023
Diophantus: A Short Animated Biographical Video
A short biographical video on Diophantus, a 3rd-century Greek mathematician, examining his life and contributions to mathematics. #history #documentary #film #biography #inspiration #Shorts #fyp #Reels #ai #art #gpt #elevenlabs #midjourney
published: 21 Jul 2023
Diophantus: Determinate and Indeterminate Equations
An introduction to some Diophantine problems, including the one that inspired Fermat.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
published: 21 May 2020
An equation Diophantus never considered.
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published: 19 Sep 2023
Math History 4.5 Diophantus and Greek Algebra
We investigate the Father of Algebra: Diophantus of Alexandria.
Movavi software was used in the creation of this video: link https://www.movavi.com/.
Diophantus of Alexandria is an important figure in the history of math. Watch to find out more!
For further reference check out:
https://en.wikipedia.org/wiki/...
Diophantus of Alexandria is an important figure in the history of math. Watch to find out more!
For further reference check out:
https://en.wikipedia.org/wiki/Diophantus
http://www-history.mcs.st-and.ac.uk/Biographies/Diophantus.html
https://www.famousscientists.org/diophantus/
https://en.wikipedia.org/wiki/Metrodorus_(grammarian)
https://www.famousmathematicians.net/diophantus/
https://en.wikipedia.org/wiki/History_of_mathematical_notation
https://www.metmuseum.org/toah/hd/roem/hd_roem.htm
Diophantus of Alexandria is an important figure in the history of math. Watch to find out more!
For further reference check out:
https://en.wikipedia.org/wiki/Diophantus
http://www-history.mcs.st-and.ac.uk/Biographies/Diophantus.html
https://www.famousscientists.org/diophantus/
https://en.wikipedia.org/wiki/Metrodorus_(grammarian)
https://www.famousmathematicians.net/diophantus/
https://en.wikipedia.org/wiki/History_of_mathematical_notation
https://www.metmuseum.org/toah/hd/roem/hd_roem.htm
Introduces what we know about Diophantus' life and the structure of his main work (the 'Arithmetica'), and outline the partial survival of his work and the hist...
Introduces what we know about Diophantus' life and the structure of his main work (the 'Arithmetica'), and outline the partial survival of his work and the history of its influence, including on Fermat's Last Theorem.
Introduces what we know about Diophantus' life and the structure of his main work (the 'Arithmetica'), and outline the partial survival of his work and the history of its influence, including on Fermat's Last Theorem.
This is a short, animated visual proof of Diophantus's sum of squares identity (also sometimes called the Brahmagupta–Fibonacci identity) using "Garfield's trap...
This is a short, animated visual proof of Diophantus's sum of squares identity (also sometimes called the Brahmagupta–Fibonacci identity) using "Garfield's trapezoid" and scaling of right triangles.
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
To see a related proof of the Cauchy-Schwarz inequality, check out:
https://youtu.be/OWR6QCPYjqI
This animation is based on a visual proof by Roger Nelsen from the April 2017 issue of Mathematics Magazine (https://doi.org/10.4169/math.mag.90.2.134 - page 134).
#math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #diophantus #algebraicidentity #mathshorts #mathvideo #mtbos #triangle #scaling #garfieldtrapezoid #trapezoid #identity
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
Kiss the Sky by Aakash Gandhi
This is a short, animated visual proof of Diophantus's sum of squares identity (also sometimes called the Brahmagupta–Fibonacci identity) using "Garfield's trapezoid" and scaling of right triangles.
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
To see a related proof of the Cauchy-Schwarz inequality, check out:
https://youtu.be/OWR6QCPYjqI
This animation is based on a visual proof by Roger Nelsen from the April 2017 issue of Mathematics Magazine (https://doi.org/10.4169/math.mag.90.2.134 - page 134).
#math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #diophantus #algebraicidentity #mathshorts #mathvideo #mtbos #triangle #scaling #garfieldtrapezoid #trapezoid #identity
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
Kiss the Sky by Aakash Gandhi
A short biographical video on Diophantus, a 3rd-century Greek mathematician, examining his life and contributions to mathematics. #history #documentary #film ...
A short biographical video on Diophantus, a 3rd-century Greek mathematician, examining his life and contributions to mathematics. #history #documentary #film #biography #inspiration #Shorts #fyp #Reels #ai #art #gpt #elevenlabs #midjourney
A short biographical video on Diophantus, a 3rd-century Greek mathematician, examining his life and contributions to mathematics. #history #documentary #film #biography #inspiration #Shorts #fyp #Reels #ai #art #gpt #elevenlabs #midjourney
An introduction to some Diophantine problems, including the one that inspired Fermat.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuz...
An introduction to some Diophantine problems, including the one that inspired Fermat.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
An introduction to some Diophantine problems, including the one that inspired Fermat.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
Diophantus of Alexandria is an important figure in the history of math. Watch to find out more!
For further reference check out:
https://en.wikipedia.org/wiki/Diophantus
http://www-history.mcs.st-and.ac.uk/Biographies/Diophantus.html
https://www.famousscientists.org/diophantus/
https://en.wikipedia.org/wiki/Metrodorus_(grammarian)
https://www.famousmathematicians.net/diophantus/
https://en.wikipedia.org/wiki/History_of_mathematical_notation
https://www.metmuseum.org/toah/hd/roem/hd_roem.htm
Introduces what we know about Diophantus' life and the structure of his main work (the 'Arithmetica'), and outline the partial survival of his work and the history of its influence, including on Fermat's Last Theorem.
This is a short, animated visual proof of Diophantus's sum of squares identity (also sometimes called the Brahmagupta–Fibonacci identity) using "Garfield's trapezoid" and scaling of right triangles.
If you like this video, consider subscribing to the channel or consider buying me a coffee: https://www.buymeacoffee.com/VisualProofs. Thanks!
To see a related proof of the Cauchy-Schwarz inequality, check out:
https://youtu.be/OWR6QCPYjqI
This animation is based on a visual proof by Roger Nelsen from the April 2017 issue of Mathematics Magazine (https://doi.org/10.4169/math.mag.90.2.134 - page 134).
#math #inequality #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #iteachmath #algebra #areas #mathematics #diophantus #algebraicidentity #mathshorts #mathvideo #mtbos #triangle #scaling #garfieldtrapezoid #trapezoid #identity
To learn more about animating with manim, check out:
https://manim.community
_____________________________
Music in this video:
Kiss the Sky by Aakash Gandhi
A short biographical video on Diophantus, a 3rd-century Greek mathematician, examining his life and contributions to mathematics. #history #documentary #film #biography #inspiration #Shorts #fyp #Reels #ai #art #gpt #elevenlabs #midjourney
An introduction to some Diophantine problems, including the one that inspired Fermat.
For more math, subscribe to my channel: https://www.youtube.com/jeffsuzuki1
Diophantus of Alexandria (Ancient Greek: Διόφαντος ὁ Ἀλεξανδρεύς; born probably sometime between AD 201 and 215; died aged 84, probably sometime between AD 285 and 299), sometimes called "the father of algebra", was an AlexandrianGreek mathematician and the author of a series of books called Arithmetica, many of which are now lost. These texts deal with solving algebraic equations. While reading Claude Gaspard Bachet de Méziriac's edition of Diophantus' Arithmetica,Pierre de Fermat concluded that a certain equation considered by Diophantus had no solutions, and noted in the margin without elaboration that he had found "a truly marvelous proof of this proposition," now referred to as Fermat's Last Theorem. This led to tremendous advances in number theory, and the study of Diophantine equations ("Diophantine geometry") and of Diophantine approximations remain important areas of mathematical research. Diophantus coined the term παρισότης (parisotes) to refer to an approximate equality. This term was rendered as adaequalitas in Latin, and became the technique of adequality developed by Pierre de Fermat to find maxima for functions and tangent lines to curves. Diophantus was the first Greek mathematician who recognized fractions as numbers; thus he allowed positiverational numbers for the coefficients and solutions. In modern use, Diophantine equations are usually algebraic equations with integer coefficients, for which integer solutions are sought. Diophantus also made advances in mathematical notation.
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