How did Ruffini discover his method of polynomial division?
How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
mathematics discoveries elementary-algebra
edited 3 hours ago
Conifold
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
mathematics discoveries elementary-algebra
edited 3 hours ago
Conifold
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
mathematics discoveries elementary-algebra
edited 3 hours ago
Conifold
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
How did Ruffini discover his method of polynomial division? At that time was it known that polynomial division works similar to integer division?
mathematics discoveries elementary-algebra
mathematics discoveries elementary-algebra
edited 3 hours ago
Conifold
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
Conifold
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
edited 3 hours ago
Conifold
32.1k150120
edited 3 hours ago
Conifold
32.1k150120
edited 3 hours ago
Conifold
32.1k150120
32.1k150120
asked 6 hours ago
user629353
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked 6 hours ago
user629353
111
asked 6 hours ago
user629353
111
111
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
user629353 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
Polynomial division algorithms were known long before Ruffini's Sopra la determinazione delle radici (1804). For a history of even older numerical division algorithms see Who invented short and long division?
Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $10$, so he may well be the first to provide a mathematical justification for a positional division algorithm.
The method for dividing by a linear factor is presented implicitly in Descartes's La Geometrie (1637), where it is used for as part of his algebraic algorithm for drawing tangents to algebraic curves (described in Is there a 'lost calculus'?). A more efficient algorithm of polynomial division, an optimized version of synthetic division, was produced by Jan Hudde in a letter included into 1659 edition of Descartes's La Geometrie, see a description in Suzuki's The Lost Calculus (1637–1670). Hudde was a talented Dutch mathematician who had to abandon mathematics for politics to save Netherlands from Spanish invasion. Ruffini's rule is an adaptation of Hudde's, see Ruffini’s Rule and meaning of division post.
What Ruffini describes generalizes to the modern synthetic division algorithm for polynomials, see Fitzherbert's Ghosts of mathematicians past: Paolo Ruffini. For subsequent generalizations by Budan and Horner see Chabert's History of Algorithms, 7.9. As a method of finding roots, historians trace the Ruffini–Horner scheme to the Chinese mathematician Jia Xian (ca. 1010–ca. 1070), who lived even earlier than al-Samaw'al, see Similarities between Chinese and Arabic Mathematical Writings: (I) Root extraction by Chemla.
answered 3 hours ago
Conifold
32.1k150120
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "587"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
user629353 is a new contributor. Be nice, and check out our Code of Conduct.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fhsm.stackexchange.com%2fquestions%2f8121%2fhow-did-ruffini-discover-his-method-of-polynomial-division%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
Polynomial division algorithms were known long before Ruffini's Sopra la determinazione delle radici (1804). For a history of even older numerical division algorithms see Who invented short and long division?
Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $10$, so he may well be the first to provide a mathematical justification for a positional division algorithm.
The method for dividing by a linear factor is presented implicitly in Descartes's La Geometrie (1637), where it is used for as part of his algebraic algorithm for drawing tangents to algebraic curves (described in Is there a 'lost calculus'?). A more efficient algorithm of polynomial division, an optimized version of synthetic division, was produced by Jan Hudde in a letter included into 1659 edition of Descartes's La Geometrie, see a description in Suzuki's The Lost Calculus (1637–1670). Hudde was a talented Dutch mathematician who had to abandon mathematics for politics to save Netherlands from Spanish invasion. Ruffini's rule is an adaptation of Hudde's, see Ruffini’s Rule and meaning of division post.
What Ruffini describes generalizes to the modern synthetic division algorithm for polynomials, see Fitzherbert's Ghosts of mathematicians past: Paolo Ruffini. For subsequent generalizations by Budan and Horner see Chabert's History of Algorithms, 7.9. As a method of finding roots, historians trace the Ruffini–Horner scheme to the Chinese mathematician Jia Xian (ca. 1010–ca. 1070), who lived even earlier than al-Samaw'al, see Similarities between Chinese and Arabic Mathematical Writings: (I) Root extraction by Chemla.
answered 3 hours ago
Conifold
32.1k150120
add a comment |
Polynomial division algorithms were known long before Ruffini's Sopra la determinazione delle radici (1804). For a history of even older numerical division algorithms see Who invented short and long division?
Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $10$, so he may well be the first to provide a mathematical justification for a positional division algorithm.
The method for dividing by a linear factor is presented implicitly in Descartes's La Geometrie (1637), where it is used for as part of his algebraic algorithm for drawing tangents to algebraic curves (described in Is there a 'lost calculus'?). A more efficient algorithm of polynomial division, an optimized version of synthetic division, was produced by Jan Hudde in a letter included into 1659 edition of Descartes's La Geometrie, see a description in Suzuki's The Lost Calculus (1637–1670). Hudde was a talented Dutch mathematician who had to abandon mathematics for politics to save Netherlands from Spanish invasion. Ruffini's rule is an adaptation of Hudde's, see Ruffini’s Rule and meaning of division post.
What Ruffini describes generalizes to the modern synthetic division algorithm for polynomials, see Fitzherbert's Ghosts of mathematicians past: Paolo Ruffini. For subsequent generalizations by Budan and Horner see Chabert's History of Algorithms, 7.9. As a method of finding roots, historians trace the Ruffini–Horner scheme to the Chinese mathematician Jia Xian (ca. 1010–ca. 1070), who lived even earlier than al-Samaw'al, see Similarities between Chinese and Arabic Mathematical Writings: (I) Root extraction by Chemla.
answered 3 hours ago
Conifold
32.1k150120
add a comment |
Polynomial division algorithms were known long before Ruffini's Sopra la determinazione delle radici (1804). For a history of even older numerical division algorithms see Who invented short and long division?
Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $10$, so he may well be the first to provide a mathematical justification for a positional division algorithm.
The method for dividing by a linear factor is presented implicitly in Descartes's La Geometrie (1637), where it is used for as part of his algebraic algorithm for drawing tangents to algebraic curves (described in Is there a 'lost calculus'?). A more efficient algorithm of polynomial division, an optimized version of synthetic division, was produced by Jan Hudde in a letter included into 1659 edition of Descartes's La Geometrie, see a description in Suzuki's The Lost Calculus (1637–1670). Hudde was a talented Dutch mathematician who had to abandon mathematics for politics to save Netherlands from Spanish invasion. Ruffini's rule is an adaptation of Hudde's, see Ruffini’s Rule and meaning of division post.
What Ruffini describes generalizes to the modern synthetic division algorithm for polynomials, see Fitzherbert's Ghosts of mathematicians past: Paolo Ruffini. For subsequent generalizations by Budan and Horner see Chabert's History of Algorithms, 7.9. As a method of finding roots, historians trace the Ruffini–Horner scheme to the Chinese mathematician Jia Xian (ca. 1010–ca. 1070), who lived even earlier than al-Samaw'al, see Similarities between Chinese and Arabic Mathematical Writings: (I) Root extraction by Chemla.
answered 3 hours ago
Conifold
32.1k150120
Polynomial division algorithms were known long before Ruffini's Sopra la determinazione delle radici (1804). For a history of even older numerical division algorithms see Who invented short and long division?
Some authors, see also Victor Katz's History of Mathematics (7.2.3), credit medieval Arabic mathematician al-Samaw'al (1130-1180) for inventing long division, of both polynomials and integers. Al-Samaw'al was first to use tables of coefficients to write and perform calculations with polynomials, he even allowed negative powers. He described a division method underlying the polynomial long division, although his record keeping is more akin to what is now called synthetic division. He also noted the analogy between his way of writing polynomials and the decimal positional notation, and transferred his algorithms to decimal numbers by simply replacing the variable with $10$, so he may well be the first to provide a mathematical justification for a positional division algorithm.
The method for dividing by a linear factor is presented implicitly in Descartes's La Geometrie (1637), where it is used for as part of his algebraic algorithm for drawing tangents to algebraic curves (described in Is there a 'lost calculus'?). A more efficient algorithm of polynomial division, an optimized version of synthetic division, was produced by Jan Hudde in a letter included into 1659 edition of Descartes's La Geometrie, see a description in Suzuki's The Lost Calculus (1637–1670). Hudde was a talented Dutch mathematician who had to abandon mathematics for politics to save Netherlands from Spanish invasion. Ruffini's rule is an adaptation of Hudde's, see Ruffini’s Rule and meaning of division post.
What Ruffini describes generalizes to the modern synthetic division algorithm for polynomials, see Fitzherbert's Ghosts of mathematicians past: Paolo Ruffini. For subsequent generalizations by Budan and Horner see Chabert's History of Algorithms, 7.9. As a method of finding roots, historians trace the Ruffini–Horner scheme to the Chinese mathematician Jia Xian (ca. 1010–ca. 1070), who lived even earlier than al-Samaw'al, see Similarities between Chinese and Arabic Mathematical Writings: (I) Root extraction by Chemla.
answered 3 hours ago
Conifold
32.1k150120
edited 2 hours ago
answered 3 hours ago
Conifold
32.1k150120
answered 3 hours ago
Conifold
32.1k150120
answered 3 hours ago
Conifold
32.1k150120
32.1k150120
add a comment |
add a comment |
user629353 is a new contributor. Be nice, and check out our Code of Conduct.
user629353 is a new contributor. Be nice, and check out our Code of Conduct.
user629353 is a new contributor. Be nice, and check out our Code of Conduct.
user629353 is a new contributor. Be nice, and check out our Code of Conduct.
Thanks for contributing an answer to History of Science and Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Some of your past answers have not been well-received, and you're in danger of being blocked from answering.
Please pay close attention to the following guidance:
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fhsm.stackexchange.com%2fquestions%2f8121%2fhow-did-ruffini-discover-his-method-of-polynomial-division%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
