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Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in 1949 to form the ISO Recommendation R3, first published in 1953 or 1954, which evolved into the international standard ISO 3.The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. One application of the

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rdfs:label	Renard-Serie (de) Serie di Rénard (it) Renard series (en) Séries de Renard (pt)
rdfs:comment	As séries de Renard são um sistema de números preferenciais que dividem um intervalo de 1 a 10 em 5, 10, 20 ou 40 passos. Este conjunto de números preferenciais foi proposto em 1877 pelo engenheiro do exército francês, coronel Charles Renard. Seu sistema foi adotado pela ISO em 1949 para formar a Recomendação ISO R3, publicada pela primeira vez em 1953 ou 1954, que evoluiu para o padrão internacional ISO 3. (pt) Eine Renard-Serie ist eine geometrische Folge von Zahlen, die allgemein als Normzahlen bezeichnet werden und in den Normen ISO 3 und DIN 323 spezifiziert sind. Eine solche Serie beginnt mit der Zahl 1 (oder 10, 100, ..) und enthält in jedem Dezimalbereich verschieden viele weitere Zahlen:Serie R5: 5 Zahlen (1; 1,6; 2,5; 4; 6,3; (10)),Serie R10: 10 Zahlen,Serie R20: 20 Zahlen,Serie R40: 40 Zahlen.Die nächstfolgende Zahl ergibt sich aus der vorherigen durch Multiplikation mit (m = 5, 10, 20 bzw. 40). Bei der praktischen Anwendung werden die Zahlen der Serien, die länger als R5 sind, gerundet (umso stärker, je länger die Serie). (de) Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in 1949 to form the ISO Recommendation R3, first published in 1953 or 1954, which evolved into the international standard ISO 3.The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. One application of the (en) La serie di Rénard di ordine k è la successione geometrica iniziante con il numero 1 e in cui il (k+1)-esimo elemento è il numero 10; nella successione l'n-esimo termine differisce dal precedente (n-1)esimo per un fattore pari alla radice k-sima di 10. In termini matematici si può definire come: oppure mediante una definizione ricorsiva come la successione geometrica che inizia per e che ha ragione : (it)
dct:subject	Industrial design Numbers Logarithmic scales of measurement
Wikipage page ID	2253990 (xsd:integer)
Wikipage revision ID	1122153147 (xsd:integer)
Link from a Wikipage to another Wikipage	Preferred number Preferred numbers English wine cask units Neper Decibel Charles Renard Institute of Radio Engineers International standard Preferred metric sizes 1-2-5 series Geometric progression Fuse (electrical) Gallon Proceedings of the IRE Proceedings of the Institute of Radio Engineers Logarithm Phon Tun (unit) E series (preferred numbers) Industrial design Foot (unit) Barrel (unit) Nominal Pipe Size Puncheon (unit) Numbers Logarithmic scales of measurement Hogshead Tierce (unit) Butt (unit) ISO Inch Metre Millimetre Rundlet International Standards Organization SI The American Society of Mechanical Engineers Relative error Geometric sequence
Link from a Wikipage to an external page	https://archive.org/stream/sizestandardizat00hirsiala%23page/n1/mode/1up https://www.forgottenbooks.com/en/download/SizeStandardizationbyPreferredNumbers_10296778.pdf%3C!-- https://web.archive.org/web/20171102224132/https:/www.iso.org/standard/4548.html https://www.iso.org/standard/4548.html
sameAs	Renard series Renard series Renard series Renard series Renard series Renard series
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Cite_journal dbt:Col-begin dbt:Col-break dbt:Col-end dbt:ISO_standards dbt:Radic dbt:Reflist dbt:Short_description dbt:Sup dbt:Use_dmy_dates
cs1-dates	y (en)
date	May 2019 (en)
has abstract	Eine Renard-Serie ist eine geometrische Folge von Zahlen, die allgemein als Normzahlen bezeichnet werden und in den Normen ISO 3 und DIN 323 spezifiziert sind. Eine solche Serie beginnt mit der Zahl 1 (oder 10, 100, ..) und enthält in jedem Dezimalbereich verschieden viele weitere Zahlen:Serie R5: 5 Zahlen (1; 1,6; 2,5; 4; 6,3; (10)),Serie R10: 10 Zahlen,Serie R20: 20 Zahlen,Serie R40: 40 Zahlen.Die nächstfolgende Zahl ergibt sich aus der vorherigen durch Multiplikation mit (m = 5, 10, 20 bzw. 40). Bei der praktischen Anwendung werden die Zahlen der Serien, die länger als R5 sind, gerundet (umso stärker, je länger die Serie). Die geometrische Abstufung erweist sich in der Praxis (z. B. im Maschinenbau) insofern als zweckmäßig, dass zwischen den Abmessungen ähnlicher kleinerer Teile (z. B. Schrauben-Längen) und Formen (z. B. Bohrungs-Durchmesser) ein kleinerer arithmetischer Abstand besteht als bei größeren Teilen und Formen. Ein Beispiel sind die kleineren Abstände zwischen den Gewindedurchmessern bei M4, M5, M6 … gegenüber den größeren zwischen den Gewindedurchmessern bei M8, M10, M12. Eine Renard-Serie wird kurz auch als R-Reihe bezeichnet. Die besonderen, für elektrische Bauelemente angewendeten Renard-Serien werden E-Reihen genannt. (de) Renard series are a system of preferred numbers dividing an interval from 1 to 10 into 5, 10, 20, or 40 steps. This set of preferred numbers was proposed in 1877 by French army engineer Colonel Charles Renard. His system was adopted by the ISO in 1949 to form the ISO Recommendation R3, first published in 1953 or 1954, which evolved into the international standard ISO 3.The factor between two consecutive numbers in a Renard series is approximately constant (before rounding), namely the 5th, 10th, 20th, or 40th root of 10 (approximately 1.58, 1.26, 1.12, and 1.06, respectively), which leads to a geometric sequence. This way, the maximum relative error is minimized if an arbitrary number is replaced by the nearest Renard number multiplied by the appropriate power of 10. One application of the Renard series of numbers is to current rating of electric fuses. Another common use is the voltage rating of capacitors (e.g. 100 V, 160 V, 250 V, 400 V, 630 V). (en) La serie di Rénard di ordine k è la successione geometrica iniziante con il numero 1 e in cui il (k+1)-esimo elemento è il numero 10; nella successione l'n-esimo termine differisce dal precedente (n-1)esimo per un fattore pari alla radice k-sima di 10. In termini matematici si può definire come: oppure mediante una definizione ricorsiva come la successione geometrica che inizia per e che ha ragione : dove sta per -esimo termine della serie di Rénard di ordine . Si indica con la successione costituita dai valori , talvolta indicati anche come . Ad esempio anche indicato come è un valore uguale a , anche indicato come è un valore pari a e così via. Questa successione ha una importanza particolare in ambito tecnico: alcune serie di Rénard sono da più di un secolo usate per esempio in costruzione di macchine per il dimensionamento geometrico delle macchine, e sono ormai state adottate come standard ISO 3 dal 1952. (it) As séries de Renard são um sistema de números preferenciais que dividem um intervalo de 1 a 10 em 5, 10, 20 ou 40 passos. Este conjunto de números preferenciais foi proposto em 1877 pelo engenheiro do exército francês, coronel Charles Renard. Seu sistema foi adotado pela ISO em 1949 para formar a Recomendação ISO R3, publicada pela primeira vez em 1953 ou 1954, que evoluiu para o padrão internacional ISO 3. (pt)
prov:wasDerivedFrom	wikipedia-en:Renard_series?oldid=1122153147&ns=0
page length (characters) of wiki page	25353 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Renard_series
is Link from a Wikipage to another Wikipage of	Preferred number Mesh (scale) Renard numbers DIN 323 Preferred metric sizes Recommendation R17 Recommendation R17-1955 Recommendation R17-1956 Recommendation R3 Recommendation R3-1953 Recommendation R3-1954 Recommendation R497 Recommendation R497-1966 Drill bit sizes E series of preferred numbers Amendment R17/A1-1966 R series (number series) 2017 in India

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