Some remarks on Bürgi’s interpolations
Identifieur interne : 000022 ( Main/Exploration ); précédent : 000021; suivant : 000023Some remarks on Bürgi’s interpolations
Auteurs : Denis Roegel [France]Source :
English descriptors
- mix :
Abstract
Jost Bürgi (1552-1632) was one of the first ones to have used the calculus of differences in order to construct a table of sines. His table of sines at 2'' intervals is lost, but in these notes, we first examine empirically (as Bürgi could have done) the influence of the number of places on the accuracy of the interpolations, and we provide two tentative interpolations for the hypothetical 2'' table.
Url:
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Hal, to step Corpus: 004654
- to stream Hal, to step Curation: 004654
- to stream Hal, to step Checkpoint: 000022
- to stream Main, to step Merge: 000022
- to stream Main, to step Curation: 000022
Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en">Some remarks on Bürgi’s interpolations</title>
<author><name sortKey="Roegel, Denis" sort="Roegel, Denis" uniqKey="Roegel D" first="Denis" last="Roegel">Denis Roegel</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-206041" status="VALID"><orgName>Proof-oriented development of computer-based systems</orgName>
<orgName type="acronym">MOSEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/equipes/mosel</ref>
</desc>
<listRelation><relation active="#struct-423084" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-423084" type="direct"><org type="department" xml:id="struct-423084" status="VALID"><orgName>Department of Formal Methods </orgName>
<orgName type="acronym">LORIA - FM</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/formal-methods</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</titleStmt>
<publicationStmt><idno type="wicri:source">HAL</idno>
<idno type="RBID">Hal:hal-01316361</idno>
<idno type="halId">hal-01316361</idno>
<idno type="halUri">https://hal.inria.fr/hal-01316361</idno>
<idno type="url">https://hal.inria.fr/hal-01316361</idno>
<date when="2016-05-16">2016-05-16</date>
<idno type="wicri:Area/Hal/Corpus">004654</idno>
<idno type="wicri:Area/Hal/Curation">004654</idno>
<idno type="wicri:Area/Hal/Checkpoint">000022</idno>
<idno type="wicri:explorRef" wicri:stream="Hal" wicri:step="Checkpoint">000022</idno>
<idno type="wicri:Area/Main/Merge">000022</idno>
<idno type="wicri:Area/Main/Curation">000022</idno>
<idno type="wicri:Area/Main/Exploration">000022</idno>
</publicationStmt>
<sourceDesc><biblStruct><analytic><title xml:lang="en">Some remarks on Bürgi’s interpolations</title>
<author><name sortKey="Roegel, Denis" sort="Roegel, Denis" uniqKey="Roegel D" first="Denis" last="Roegel">Denis Roegel</name>
<affiliation wicri:level="1"><hal:affiliation type="researchteam" xml:id="struct-206041" status="VALID"><orgName>Proof-oriented development of computer-based systems</orgName>
<orgName type="acronym">MOSEL</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/equipes/mosel</ref>
</desc>
<listRelation><relation active="#struct-423084" type="direct"></relation>
<relation active="#struct-206040" type="indirect"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
<tutelles><tutelle active="#struct-423084" type="direct"><org type="department" xml:id="struct-423084" status="VALID"><orgName>Department of Formal Methods </orgName>
<orgName type="acronym">LORIA - FM</orgName>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr/la-recherche-en/departements/formal-methods</ref>
</desc>
<listRelation><relation active="#struct-206040" type="direct"></relation>
<relation active="#struct-300009" type="indirect"></relation>
<relation active="#struct-413289" type="indirect"></relation>
<relation name="UMR7503" active="#struct-441569" type="indirect"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-206040" type="indirect"><org type="laboratory" xml:id="struct-206040" status="VALID"><idno type="IdRef">067077927</idno>
<idno type="RNSR">198912571S</idno>
<idno type="IdUnivLorraine">[UL]RSI--</idno>
<orgName>Laboratoire Lorrain de Recherche en Informatique et ses Applications</orgName>
<orgName type="acronym">LORIA</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>Campus Scientifique BP 239 54506 Vandoeuvre-lès-Nancy Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.loria.fr</ref>
</desc>
<listRelation><relation active="#struct-300009" type="direct"></relation>
<relation active="#struct-413289" type="direct"></relation>
<relation name="UMR7503" active="#struct-441569" type="direct"></relation>
</listRelation>
</org>
</tutelle>
<tutelle active="#struct-300009" type="indirect"><org type="institution" xml:id="struct-300009" status="VALID"><orgName>Institut National de Recherche en Informatique et en Automatique</orgName>
<orgName type="acronym">Inria</orgName>
<desc><address><addrLine>Domaine de VoluceauRocquencourt - BP 10578153 Le Chesnay Cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.inria.fr/en/</ref>
</desc>
</org>
</tutelle>
<tutelle active="#struct-413289" type="indirect"><org type="institution" xml:id="struct-413289" status="VALID"><idno type="IdRef">157040569</idno>
<idno type="IdUnivLorraine">[UL]100--</idno>
<orgName>Université de Lorraine</orgName>
<orgName type="acronym">UL</orgName>
<date type="start">2012-01-01</date>
<desc><address><addrLine>34 cours Léopold - CS 25233 - 54052 Nancy cedex</addrLine>
<country key="FR"></country>
</address>
<ref type="url">http://www.univ-lorraine.fr/</ref>
</desc>
</org>
</tutelle>
<tutelle name="UMR7503" active="#struct-441569" type="indirect"><org type="institution" xml:id="struct-441569" status="VALID"><idno type="ISNI">0000000122597504</idno>
<idno type="IdRef">02636817X</idno>
<orgName>Centre National de la Recherche Scientifique</orgName>
<orgName type="acronym">CNRS</orgName>
<date type="start">1939-10-19</date>
<desc><address><country key="FR"></country>
</address>
<ref type="url">http://www.cnrs.fr/</ref>
</desc>
</org>
</tutelle>
</tutelles>
</hal:affiliation>
<country>France</country>
<placeName><settlement type="city">Nancy</settlement>
<settlement type="city">Metz</settlement>
<region type="region" nuts="2">Grand Est</region>
<region type="old region" nuts="2">Lorraine (région)</region>
</placeName>
<orgName type="university">Université de Lorraine</orgName>
</affiliation>
</author>
</analytic>
</biblStruct>
</sourceDesc>
</fileDesc>
<profileDesc><textClass><keywords scheme="mix" xml:lang="en"><term> Babbage</term>
<term> Prony</term>
<term> cadastre</term>
<term> calculus of differences</term>
<term> interpolation</term>
<term> tables of sines</term>
<term>Jost Bürgi</term>
</keywords>
</textClass>
</profileDesc>
</teiHeader>
<front><div type="abstract" xml:lang="en">Jost Bürgi (1552-1632) was one of the first ones to have used the calculus of differences in order to construct a table of sines. His table of sines at 2'' intervals is lost, but in these notes, we first examine empirically (as Bürgi could have done) the influence of the number of places on the accuracy of the interpolations, and we provide two tentative interpolations for the hypothetical 2'' table.</div>
</front>
</TEI>
<affiliations><list><country><li>France</li>
</country>
<region><li>Grand Est</li>
<li>Lorraine (région)</li>
</region>
<settlement><li>Metz</li>
<li>Nancy</li>
</settlement>
<orgName><li>Université de Lorraine</li>
</orgName>
</list>
<tree><country name="France"><region name="Grand Est"><name sortKey="Roegel, Denis" sort="Roegel, Denis" uniqKey="Roegel D" first="Denis" last="Roegel">Denis Roegel</name>
</region>
</country>
</tree>
</affiliations>
</record>
Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Lorraine/explor/InforLorV4/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000022 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 000022 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien |wiki= Wicri/Lorraine |area= InforLorV4 |flux= Main |étape= Exploration |type= RBID |clé= Hal:hal-01316361 |texte= Some remarks on Bürgi’s interpolations }}
This area was generated with Dilib version V0.6.33. |