Dinostratus

Dinostratus
Born	c. 390 BCE
Died	c. 320 BCE
Nationality	Greek
Known for	Quadratrix of Dinostratus Dinostratus' theorem
Scientific career
Fields	Mathematics

Dinostratus (Greek: Δεινόστρατος; c. 390 – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle.

Life and work

Dinostratus' chief contribution to mathematics was his solution to the problem of squaring the circle. To solve this problem, Dinostratus made use of the trisectrix of Hippias, for which he proved a special property (Dinostratus' theorem) that allowed him the squaring of the circle. Due to his work the trisectrix later became known as the quadratrix of Dinostratus as well.^[1] Although Dinostratus solved the problem of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics.^[1] Over 2,200 years later Ferdinand von Lindemann would prove that it is impossible to square a circle using straight edge and compass alone.

Citations and footnotes

^ ^a ^b Boyer (1991). "The age of Plato and Aristotle". A History of Mathematics. Wiley. pp. 96–97. ISBN 9780471543978. Dinostratus, brother of Menaechmus, was also a mathematician, and where one of the brothers "solved" the duplication of the cube, the other "solved" the squaring of the circle. The quadrature because a simple matter once a striking property of the end point Q of the trisectrix of Hippias had been noted, apparently by Dinostratus. If the equation of the trisectrix (Fig. 6.4) is πrsin θ = 2aθ, where a is the side of the square ABCD associated with the curve, [...] hence, Dinostratus' theorem is established - that is, AC/AB = AB/DQ. [...] Inasmuch as Dinostratus showed that the trisectrix of Hippias serves to square the circle, the curve more commonly came to be known as the quadratrix. It was, of course, always clear to the Greeks that the use of the curve in the trisection and quadrature problems violated the rules of the game - that circles and straight lines only were permitted. The "solution" of Hippias and Dinostratus, as their authors realized, were sophistic; hence, the search for further solutions, canonical or illegitimate, continued with the result that several new curves were discovered by Greek geometers.

References

Boyer, Carl B. (1991). A History of Mathematics (Second ed.). John Wiley & Sons, Inc. ISBN 0-471-54397-7.

External links

O'Connor, John J.; Robertson, Edmund F., "Dinostratus", MacTutor History of Mathematics Archive, University of St Andrews

Ancient Greek mathematics

Mathematicians
(timeline)

Treatises

Problems

Concepts
and definitions

Results

In Elements	Angle bisector theorem Exterior angle theorem Euclidean algorithm Euclid's theorem Geometric mean theorem Greek geometric algebra Hinge theorem Inscribed angle theorem Intercept theorem Intersecting chords theorem Intersecting secants theorem Law of cosines Pons asinorum Pythagorean theorem Tangent-secant theorem Thales's theorem Theorem of the gnomon
Apollonius	Apollonius's theorem
Other	Aristarchus's inequality Crossbar theorem Heron's formula Irrational numbers Law of sines Menelaus's theorem Pappus's area theorem Problem II.8 of Arithmetica Ptolemy's inequality Ptolemy's table of chords Ptolemy's theorem Spiral of Theodorus

Centers

Ancient Greek astronomy Attic numerals Greek numerals Latin translations of the 12th century Non-Euclidean geometry Philosophy of mathematics Neusis construction
History of	A History of Greek Mathematics by Thomas Heath algebra timeline arithmetic timeline calculus timeline geometry timeline logic timeline mathematics timeline numbers prehistoric counting numeral systems list
Other cultures	Arabian/Islamic Babylonian Chinese Egyptian Incan Indian Japanese

Ancient Greece portal • Mathematics portal

Read other articles:

Cachan

CachanNegaraPrancisArondisemenL'Haÿ-les-RosesAntarkomuneCommunautéd'agglomérationde Val de Bièvre Cachan merupakan sebuah komune di pinggiran selatan Paris, Prancis. Terletak 6.7 km (4.2 mil) dari pusat kota Paris. École Normale Supérieure de Cachan terletak di sini. Nama Pada Abad Pertengahan, Cachan tercantum dalam teks Latin Pertengahan sebagai Caticantum, kemudian berubah menjadi Cachentum, Cachant, dan kemudian Cachan. Beberapa orang mengetahui Caticantum berarti nyanyian kuci...

2013 Tennessee Titans season

54th season in franchise history; final one with Bud Adams 2013 Tennessee Titans seasonOwnerBud Adams (until death) KSA Industries (after October 21)General managerRuston WebsterHead coachMike MunchakHome fieldLP FieldResultsRecord7–9Division place2nd AFC SouthPlayoff finishDid not qualifyPro BowlersCB Alterraun Verner ← 2012 Titans seasons 2014 → The 2013 Tennessee Titans season was the franchise's 44th season in the National Football League (NFL), the 54th overa...

Richard Coote, 1st Earl of Bellomont

MP and colonial governor The Right HonourableThe Earl of BellomontEngraved portrait of the earl, c. 188812th Governor of the Province of New YorkIn office1698–1700/01MonarchsWilliam III and Mary IIPreceded byBenjamin FletcherSucceeded byJohn Nanfan (acting)2nd Governor of the Province of Massachusetts BayIn office26 May 1699 – 17 July 1700Preceded byWilliam Stoughton (acting)Succeeded byWilliam Stoughton (acting)Governor of the Province of New HampshireIn office31 J...

Primate cognition

Study of non-human primate intellect 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: Primate cognition – news · newspapers · books · scholar · JSTOR (March 2012) (Learn how and when to remove this template message) The Chimpanzee Böbe in 1967 Böbe painting in 1967 Primate cognition is the study of the inte...

Molineuf

Molineuf L'église Saint-Secondin. Administration Pays France Région Centre-Val de Loire Département Loir-et-Cher Arrondissement Blois Intercommunalité Agglopolys Statut Commune déléguée Maire délégué Mandat Christine Pavy 2020-2026 Code postal 41190 Code commune 41142 Démographie Gentilé Molineuvois Population 784 hab. (2013) Densité 71 hab./km2 Géographie Coordonnées 47° 34′ 46″ nord, 1° 12′ 58″ est Altitude Min. 72 mMax....

Nirmala Dewi

Artikel ini sebatang kara, artinya tidak ada artikel lain yang memiliki pranala balik ke halaman ini.Bantulah menambah pranala ke artikel ini dari artikel yang berhubungan atau coba peralatan pencari pranala.Tag ini diberikan pada Oktober 2022. Nirmala DewiKebangsaanIndonesiaPekerjaanSekretaris JenderalOrganisasiPengurus Pusat Persatuan Bolabasket Seluruh Indonesia (PP PERBASI) Nirmala Dewi adalah perempuan pertama yang menjabat sebagai Sekretaris Jenderal Pengurus Pusat Persatuan Bolabasket ...

Stadion Renato Dall'Ara

Stadion Renato Dall'Ara Informasi stadionNama lamaStadion Littoriale (1927–1945)Stadion Comunale (1945–1983)PemilikPemerintah Kota BolognaLokasiLokasiVia Andrea Costa174, 40134 Bologna ItalyKoordinat44°29′32.33″N 11°18′34.80″E / 44.4923139°N 11.3096667°E / 44.4923139; 11.3096667Koordinat: 44°29′32.33″N 11°18′34.80″E / 44.4923139°N 11.3096667°E / 44.4923139; 11.3096667KonstruksiMulai pembangunan1925Dibuka1927Data ...

Brecknockshire

Historic county of Wales Breconshire redirects here. For other uses, see Breconshire (disambiguation). BrecknockshireBrycheiniog or Sir Frycheiniog (Welsh) Show location in Wales Show location in England and Wales Show location in the United KingdomArea • 1831460,158 acres (1,862.19 km2) • 1911469,281 acres (1,899.11 km2) • 1961469,281 acres (1,899.11 km2) Population • 183147,763[1] • 190154,213 •&#...

AH83

Asian Highway 83 (AH83) adalah bagian dari Jaringan Jalan Asia sejauh 172 km (107.5 mil) dari Qazax, Azerbaijan ke Yerevan, Armenia. Rute yang dilewati adalah: Azerbaijan R23 R23 Road: Qazax - Bala Cəfərli Armenia Մ 4 M-4 Highway: Paravakar - Yerevan lbsJaringan Jalan AsiaSeluruh benua AH1 AH2 AH3 AH4 AH5 AH6 AH7 AH8 Asia Tenggara AH11 AH12 AH13 AH14 AH15 AH16 AH18 AH19 AH25 AH26 AH140 AH141 AH142 AH143 AH150 Asia Timur, Asia Timur Laut, dan Asia Tenggara AH30 AH31 AH32 AH33 AH34 Anak...

ضريح حكيم نزاري

ضريح حكيم نزاريمعلومات عامةنوع المبنى ضريح البلد إيران المدينة بيرجندتعديل - تعديل مصدري - تعديل ويكي بيانات ضريح الملا هادي السبزوري (بالفارسية: آرامگاه ملا هادی سبزواری) ضريح تاريخي، يقع في بيرجند. هذا المبنى هو قبر نزاري القهستاني.[1] مراجع ^ Encyclopaedia of the Iranian Architectura...

Battle of Lysychansk

Battle in the Russian invasion of Ukraine Battle of LysychanskPart of the battle of Donbas during the eastern Ukraine campaignPro-Russian separatist troops advance towards LysychanskDate25 June – 2/3 July 2022 (1 week and 1 day)LocationLysychansk, Luhansk Oblast, UkraineResult Russian and LPR victory[1]Territorialchanges Russian and LPR forces capture Lysychansk, Novodruzhesk, Maloriazantseve and Bila Hora[2] Russian and LPR forces fully occupy Luhansk Oblast for a...

تايوان

هذه المقالة عن جمهورية الصين (تايوان). للجمهورية الصينية الشعبية (الصين)، طالع جمهورية الصين الشعبية. هذه المقالة عن تايوان المسماة قديمًا فرموزة أو فورموزا. لمعانٍ أخرى، طالع فورموزا (توضيح). جمهورية الصين (بالصينية: 中華民國) تايوانعلم تايوان تايوانشعار جمه...

Tenente colonnello

Tenente colonnello è, nella gerarchia militare, un Grado della categoria degli Ufficiali Superiori posto fra quello di Maggiore (di livello inferiore) e di Colonnello (superiore). Al grado di Tenente Colonnello corrisponde il comando di un Battaglione o di una Unità equivalente (Gruppo Squadroni per la Cavalleria e l'Aviazione dell'Esercito, Gruppo per l'Artiglieria). Lo sviluppo organico dei Reparti e l'aumentare delle competenze, che portò mutamenti, integrazioni e aumenti nelle figure g...

Linear Elamite

Writing system from Elam Linear ElamiteLinear Elamite characters inventoried by 1912.[1]Script type Semisyllabary [a] or logosyllabic[b]Time periodc. 2300–1850 BCEStatusExtinctDirectionLeft-to-right, right-to-left script LanguagesElamiteRelated scriptsParent systemsProto-writingProto-Elamite?Linear Elamite Linear Elamite was a writing system used in Elam during the Bronze Age between c. 2300 and 1850 BCE, and known mainly from a few extant monumental...

حادثة مكة 1987

حادثة مكة 1987 المتظاهرون في أحد الشوارع قرب الحرم المكي المعلومات البلد السعودية الإحداثيات 21°26′07″N 39°49′45″E / 21.4353°N 39.8291°E / 21.4353; 39.8291 التاريخ 31 يوليو 1987 الخسائر الوفيات 402 الإصابات 649 تعديل مصدري - تعديل أحداث حج مكة 1407هـ/1987م هي اشتباكات عنيفة وقعت في...

Do Tank

Un Do Tank (expression faisant référence à celle de Think Tank) est un type de structure associative et collaborative qui émerge dans les années 2010, par opposition aux think tanks (laboratoire d'idées[1], ou groupe de réflexion [2]). Schéma montrant les notions de Think tank et de Do tank, avec entre les deux le Think and do tanks. Il s'agit d'un cercle de personnes plus ou moins experts dans le domaine, qui décident de travailler ensemble, avec une finalité non pas uniquement ori...

Awa (provincia, Chiba)

Questa voce sull'argomento storia del Giappone è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Mappa delle province giapponesi con la provincia di Awa (Chiba) evidenziata Awa (安房国?, Awa-kuni) fu una vecchia provincia del Giappone che nell'XI secolo è compresa della prefettura di Chiba. La provincia di Awa occupa la punta della penisola di Bōsō e confina con la provincia di Kazusa. Si ritiene che la vecchia capitale, Heguri-gun, si trovi vicin...

Antoine-Ulrich de Saxe-Meiningen

Antoine-Ulrich de Saxe-MeiningenAntoine Ulrich de Saxe-MeiningenTitre de noblesseDucBiographieNaissance 22 octobre 1687MeiningenDécès 27 janvier 1763 (à 75 ans)Francfort-sur-le-MainNom dans la langue maternelle Anton Ulrich von Sachsen-MeiningenFamille Duché de Saxe-MeiningenPère Bernard Ier de Saxe-MeiningenMère Élisabeth-Éléonore de Brunswick-WolfenbüttelFratrie Ernest-Louis IerFrédéric-Guillaume de Saxe-MeiningenÉlisabeth de Saxe-Meiningen (en)Wilhelmine-Louise ...

サンタンデール銀行

サンタンデール銀行Banco Santander S.A. マドリード西郊、ボアディージャ・デル・モンテのグループ本部種類公開会社市場情報 BMAD: SANNYSE: SANLSE: SANWSE: SAN本社所在地スペイン28660Santander Group City Av. de Cantabria s/n, ボアディージャ・デル・モンテ, マドリード設立 1857年 (167年前) (1857)業種銀行業代表者ホセ・アントニオ・アルバレス（CEO）外部リンクコー...

Étienne Dupérac

Remains of the Baths of Constantine in Rome, etching by Dupérac (c. 1575) Étienne Dupérac (or du Pérac) (c. 1525–March 1604) was a French architect, painter, engraver, and garden designer.[1] He is most well known for his topographical studies of Rome and its ruins in the late 16th century.[2] Rome Dupérac was born in Bordeaux[2] or Paris[3] and arrived in Rome in 1550, where he became a skilled designer and engraver.[2] He published a bird...