Piràmide quadrada

Piràmide quadrada
Elements

Model 3D
Tipus	Sòlid de Johnson
Forma de les cares	Triangles equilàters i un quadrat
Símbol de Schläfli	()∨{4}
Cares per vèrtex	3 i 4
Vèrtexs per cara	3 i 4
Simetria	C_4v
Dual	Ella mateixa
Propietats	Convex

Cares	5
Arestes	8
Vèrtexs	5

Característica	2
Més informació
MathWorld	SquarePyramid

En geometria, la piràmide quadrada és una piràmide que té un quadrat a la base.

Si el vèrtex oposat a la base quadrada està sobre la perpendicular traçada al centra del quadrat llavors té simetria C_4v

Si les cares triangulars són triangles equilàters llavors és un dels noranta-dos sòlids de Johnson (J₁).

Com totes les piràmides, és dual de si mateixa.

Els 92 sòlids de Johnson van ser descrits 1966 per Norman Johnson i els va numerar. No va demostrar que no n'existia més que 92, però va conjecturar que no n'hi havia d'altres. Victor Zalgaller el 1969 va demostrar que la llista de Johnson era completa. S'utilitzen els noms i l'ordre donats per Johnson, i se'ls nota J_xx on xx és el nombre donat per Jonson.

Superfície i volum

En general per una piràmide quadrada qualsevol amb aresta de la base de longitud l i alçada h es té que el volum V i l'àrea de les cares A és:^[1]

A=l^{2}+l{\sqrt {l^{2}+(2h)^{2}}}

V={\frac {1}{3}}l^{2}h.

Pel cas en què les cares triangulars siguin triangles equilàters (és a dir, per al cas que sigui un sòlid de Johnson d'aresta a, llavors es té:^[2]

A=(1+{\sqrt {3}})a^{2}

V={\frac {\sqrt {2}}{6}}a^{3}

A més en aquest cas l'alçada H és:

H={\frac {1}{\sqrt {2}}}a

En aquest cas, totes les arestes de la piràmide mesuren a.^[3]

Desenvolupament pla

Referències

↑ Sapiña, R. «Calculadora de l'àrea i volum de la piràmide quadrada» (en castellà). Problemas y ecuaciones. ISSN: 2659-9899 [Consulta: 26 juny 2020].
↑ Sapiña, R. «Sòlid de Johnson J₁» (en castellà). Problemas y ecuaciones. ISSN: 2659-9899 [Consulta: 26 juny 2020].
↑ Hocevar, Franz. A. & C. Black. Geometria sòlida (en anglès), 1903, p. 44.

Norman W. Johnson, "Convex Solids with Regular Faces", Canadian Journal of Mathematics, 18, 1966, pages 169–200. Conté l'enumeració original dels 92 sòlids i la conjectura que no n'hi ha d'altres.
Victor A. Zalgaller, "Convex Polyhedra with Regular Faces", 1969 : primera demostració d'aquesta conjectura.
Eric W. Weisstein. Johnson Solid : cada sòlid amb el seu desenvolupament

Vegeu també

Enllaços externs

Weistein, Eric W., Square pyramid piràmide quadrada a MathWorld. (anglès)
Weistein, Eric W., Johnson solid Sòlids de Johnson a MathWorld. (anglès)

Read other articles:

kadar air

Komposisi tanah berdasarkan fase: s = soil (tanah), (komponen kering); v = void (kosong atau rongga) (pori-pori tanah yang terisi oleh air dan/atau udara); w = water (air); a = air (udara). V adalah volume dan M adalah massa. Kadar air adalah sejumlah air yang terkandung di dalam suatu benda, seperti tanah (yang disebut juga kelembapan tanah), bebatuan, bahan pertanian, dan sebagainya. Kadar air digunakan secara luas dalam bidang ilmiah dan teknik dan diekspresikan dalam rasio, dari 0 (kering...

Harpe brothers

American criminal duo This article has multiple issues. Please help improve it or discuss these issues on the talk page. (Learn how and when to remove these template messages) This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Harpe brothers – news · newspapers · books · scholar · JSTOR (September 2018) (Learn ...

Underclass

Segment of the population that occupies the lowest possible position in a class hierarchy The examples and perspective in this article deal primarily with the United States and do not represent a worldwide view of the subject. You may improve this article, discuss the issue on the talk page, or create a new article, as appropriate. (February 2013) (Learn how and when to remove this template message) The underclass is the segment of the population that occupies the lowest possible position in ...

Darjah Kerabat Laila Utama

Darjah Kerabat Laila Utama Yang Amat Dihormati درجه قرابة لاءيلا اوتام يڠ امت دحرمتيDianugerahkan oleh Sultan BruneiTipeTanda kehormatanDibentuk1 Maret 1954Negara BruneiStatusMasih dianugerahkanGelar akhiranDKStatistikPenganugerahan pertama1954 Omar Ali Saifuddien IIIPenganugerahan terakhir2022 Lee Hsien LoongPrioritasTingkat lebih tinggiDarjah Kerabat Mahkota BruneiTingkat lebih rendahDarjah Kerabat Seri UtamaPita tanda kehormatan Darjah Kerabat Laila Utam...

Betty White

Betty WhiteWhite pada premiere The Proposal Juni 2009LahirBetty Marion White(1922-01-17)17 Januari 1922Oak Park, Illinois, Amerika SerikatMeninggal31 Desember 2021(2021-12-31) (umur 99)Los Angeles, California, Amerika SerikatPekerjaanActressTahun aktif1945 – 2021Suami/istriAllen Ludden (1963 – 1981)Lane Allen (1947 – 1949)Dick Barker (1945) Betty Marion White (17 Januari 1922 – 31 Desember 2021) adalah pemeran wanita, pelawak dan mantan pembawa acara Amerika S...

Léo Duarte

Brazilian footballer (born 1996) For the Brazilian right-back born in 1999, see Léo Duarte (footballer, born 1999). In this Portuguese name, the first or maternal family name is Duarte and the second or paternal family name is da Silva. Léo Duarte Duarte with İstanbul Başakşehir in 2022Personal informationFull name Leonardo Campos Duarte da SilvaDate of birth (1996-07-17) 17 July 1996 (age 27)Place of birth Mococa, BrazilHeight 1.83 m (6 ft 0 in)[1]Positio...

Paus Klemens I

Santo PausKlemens IUskup RomaLukisan c. 1000 di Katedral KyivGerejaGereja KatolikAwal masa kepausan88 ADAkhir masa kepausan99 ADPendahuluAnakletusPenerusEvaristusImamatTahbisan uskupoleh Santo PetrusInformasi pribadiLahirc. 35 ADRoma, Kekaisaran RomawiWafat99 AD (umur 63–64)Khersonesos, Taurike, Kerajaan BosporosOrang kudusHari heringatan23 November (Gereja Katolik)24 November (mayoritas Gereja Bizantin)25 November (Gereja Ortodoks Rusia)29 Hathor (Gereja Ortodoks Oriental)Venera...

Curtiss Robin

Curtiss Robin A Curtiss Robin in the Seattle museum of flight, 2011 Role TouringType of aircraft Manufacturer Curtiss-Robertson Airplane Manufacturing Company First flight 7 August 1928[1] Introduction 1928 Status A number still flying[1] Primary user U. S. Private Owner Market[1] Number built 769[1] The Curtiss Robin, introduced in 1928, was an American high-wing monoplane built by the Curtiss-Robertson Airplane Manufacturing Company. The J-1 version was...

Garuda 19

Garuda 19Poster filmSutradaraAndibachtiar YusufProduserPutut WidjanarkoAvesian SoebliSkenarioSwastika NoharaAndibachtiar YusufBerdasarkanSemangat Membatuoleh FX Rudi GunawanGuntur Cahyo UtomoPemeranMathias MuchusIbnu JamilYusuf MahardikaRendy AhmadGazza ZubizaretaSumarlin BetaReza AdityaVerdi Solaiman Puadin RediMandala ShojiAgri FirdausBilqis AtariAmanda KhairunnisaPenata musikNoeMerlistoSinematograferRoni ArnoldPenyuntingWawan I. WibowoPerusahaanproduksiMizan ProductionsTanggal rilis9...

Verdi Europei - Green Italia

La rilevanza enciclopedica di questa voce o sezione sull'argomento politica è stata messa in dubbio. Motivo: Lista elettorale esistita per pochi mesi e presentatasi a una sola elezione senza ottenere risultati di rilievo (nessun eletto e 0,91% dei voti). Tra le pochissime informazioni presenti in voce si dice che non riuscì neanche a raccogliere le firme per presentarsi alle europee, cosa che di certo non gioca a favore della rilevanza. Puoi aiutare aggiungendo informazioni verificabi...

Konvikt

Studienheim ist eine Weiterleitung auf diesen Artikel. Siehe auch Studienhaus und Bischöfliches Knabenseminar. Ein Konvikt (von lat. convivere; sowohl convictus, -us m. als auch convictio, -onis f. Gemeinschaft, Zusammenleben), deutsch Studienhaus oder Stift, nennt man dem Klosterleben nachgebildete, meist auf alten Stiftungen beruhende oder aus öffentlichen Mitteln unterhaltene Institute für Schüler oder Studenten im kirchlichen Bereich, mit Wohnmöglichkeit und einer gemeinsamen Hausor...

Aída Sullivan

Aída Sullivan CoyaFirst Lady of SonoraIn officeSeptember 13, 1943 – April 15, 1948GovernorAbelardo L. RodríguezFirst Lady of MexicoIn officeSeptember 4, 1932 – November 30, 1934PresidentAbelardo L. RodríguezPreceded byJosefina OrtizSucceeded byAmalia Solórzano Personal detailsBornAída Sullivan Coya(1904-04-23)April 23, 1904Puebla, Puebla state, MexicoDiedAugust 17, 1975(1975-08-17) (aged 71)Mexico City, MexicoSpouse Abelardo L. Rodríguez ...

Saison 2017 de l'équipe cycliste Riwal Platform

Riwal Platform 2017GénéralitésÉquipe Riwal Cycling TeamCode UCI RIWStatut Équipe continentalePays DanemarkSport Cyclisme sur routeEffectif 15PalmarèsNombre de victoires 1Riwal Platform 2016 (d)Riwal CeramicSpeed 2018 (d)modifier - modifier le code - modifier Wikidata La saison 2017 de l'équipe cycliste Riwal Platform est la neuvième de cette équipe. Préparation de la saison 2017 Sponsors et financement de l'équipe Cette section est vide, insuffisamment détaillée ou incompl�...

Economic history of Portugal

Portuguese Economy's history Part of a series on the History of Portugal Ancient Prehistoric Iberia Pre-Roman Peoples Roman conquest of Hispania Romanization of Hispania Lusitania Gallaecia Suebic Kingdom Visigothic Kingdom Spania Medieval Umayyad conquest of Hispania Al-Andalus Gharb Al-Andalus Almoravid dynasty County of Portugal Reconquista Portuguese House of Burgundy 1383–1385 Crisis Age of Discovery Imperial expansion House of Aviz Portuguese Renaissance Portuguese Empire War of the P...

Gom van Strien

Dutch politician (born 1951) In this Dutch name, the surname is Van Strien, not Strien. Gom van StrienGom van StrienMember of the SenateIncumbentAssumed office 7 June 2011 Personal detailsBornGommarus Adrianus van Strien (1951-06-10) 10 June 1951 (age 72)Geertruidenberg, NetherlandsPolitical partyParty for Freedom (since 2009)Other politicalaffiliationsPeople's Party for Freedom and Democracy (until 1999)Alma materKatholieke Universiteit Nijmegen University of Twente Gommarus Adrianu...

Imagine Children's Museum

Children's museum in Everett, WashingtonImagine Children's MuseumFront entrance of the museum at Wall St. and Hoyt Ave. (2004-2022)Established1991Location1502 Wall StreetEverett, WashingtonCoordinates47°58′39″N 122°12′34″W / 47.97750°N 122.20944°W / 47.97750; -122.20944TypeChildren's museumWebsitewww.imaginecm.org Imagine Children's Museum is a non-profit children's museum located in Everett, Washington, USA, near Seattle. History Front entrance of the muse...

Kenneth Stewart Cole

American biophysicist (1900–1984) Kenneth Stewart ColeBorn(1900-07-10)July 10, 1900Ithaca, New YorkDiedApril 18, 1984(1984-04-18) (aged 83)La Jolla, CaliforniaAlma materOberlin CollegeCornell UniversityKnown forCole–Cole equationVoltage clampSpouseElizabeth Evans RobertsChildren2AwardsForMemRS (1972)National Medal of Science (1967)Guggenheim Fellowship (1941)Scientific careerFieldsBiophysics Kenneth Stewart Cole (July 10, 1900 – April 18, 1984) was an American biophysicis...

Carlos Gutierrez

Si ce bandeau n'est plus pertinent, retirez-le. Cliquez ici pour en savoir plus. Cet article ne cite pas suffisamment ses sources (mars 2019). Si vous disposez d'ouvrages ou d'articles de référence ou si vous connaissez des sites web de qualité traitant du thème abordé ici, merci de compléter l'article en donnant les références utiles à sa vérifiabilité et en les liant à la section « Notes et références ». En pratique : Quelles sources sont attendues ? Comm...

Joseph Berchtold

Second commander of the SS Joseph BerchtoldBerchtold in his SA uniform2nd Reichsführer-SSIn office15 April 1926 – 1 March 1927LeaderAdolf HitlerPreceded byJulius SchreckSucceeded byErhard Heiden Personal detailsBorn6 March 1897Ingolstadt, Kingdom of Bavaria, German EmpireDied23 August 1962(1962-08-23) (aged 65)Herrsching, Bavaria, West GermanyPolitical partyNazi Party (1920–1921, 1922–1945)Other politicalaffiliationsGerman Workers' Party (1920)Military serviceAllegian...

Djimon Hounsou

Beninese-born actor (b. 1964) Djimon HounsouHounsou in 2016BornDjimon Gaston Hounsou (1964-04-24) April 24, 1964 (age 60)Cotonou, DahomeyCitizenshipBeninUnited StatesOccupationsActormodelYears active1986–presentPartnerKimora Lee Simmons (2007–2012)Children1 Djimon Gaston Hounsou (/ˈdʒaɪmən ˈuːnsuː/, JY-mən OON-soo;[1] French: [dʒimɔ̃ unsu]; born April 24, 1964)[2] is a Beninese-born actor. He began his career appearing in music videos and made ...