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Archimedean circles constructed by Thomas Schoch
the Schoch circles are twelve Archimedean circles constructed by Thomas Schoch. In 1979, Thomas Schoch discovered a dozen new Archimedean circles; he
Schoch_circles
Circle in the arbelos congruent to the twin circles
Archimedean circles called Bankoff's triplet circle and Bankoff's quadruplet circle. In 1978 Thomas Schoch found a dozen more Archimedean circles (the Schoch circles)
Archimedean_circle
Schoch line is a line defined from an arbelos and named by Peter Woo after Thomas Schoch, who had studied it in conjunction with the Schoch circles.
Schoch_line
Simple curve of Euclidean geometry
generalised circles are actually circles: a generalised circle is either a (true) circle or a line. The tangent line through a point P on the circle is perpendicular
Circle
Two congruent circles within an arbelos
called Archimedean circles. They include the Bankoff circle, Schoch circles, and Woo circles. Let a and b be the diameters of two inner semicircles, so
Twin_circles
arbelos arc. Any circle centered on the Schoch line and externally tangent to the circles is a Woo circle. Schoch circles Thomas Schoch (2007). "Arbelos
Woo_circles
Plane region bounded by three semicircles
the geometric figure. Archimedes' quadruplets Bankoff circle Schoch circles Schoch line Woo circles Pappus chain Salinon Weisstein, Eric W. "Arbelos". MathWorld
Arbelos
Schinzel circle – Theorem about circles through lattice pointsPages displaying short descriptions of redirect targets Schoch circles – Archimedean circles constructed
List_of_circle_topics
Circle constructed from an arbelos
JSTOR 2689213. Dodge, Clayton W.; Schoch, Thomas; Woo, Peter Y.; Yiu, Paul (1999), "Those ubiquitous Archimedean circles", Mathematics Magazine, 72 (3):
Bankoff_circle
1848 painting of Germania symbolizing Germany
bare sword and an olive branch. At her feet lies a burst fetlock." (Rainer Schoch) "With shattered fetters, holding the black-red-gold flag in her left hand
Germania (St. Paul's Church, Frankfurt am Main)
Germania_(St._Paul's_Church,_Frankfurt_am_Main)
Annual American award honoring Off-Broadway and Broadway theater productions
Warren Baker, Kors Le Pere Theatricals, Pamela Lloyd, Steve Peters, Suzanne Schoch Rehl & Scott Rehl, Trafalgar Entertainment, Dennis Trunfio, Viva Diva USA
Outer Critics Circle Award for Outstanding Revival of a Musical
Outer_Critics_Circle_Award_for_Outstanding_Revival_of_a_Musical
Painting by Philipp Veit (1834–1836)
artists but was apparently influenced by Veit's earlier Germania. Rainer Schoch: "Streit um Germania. Bemerkungen zur 'Germania' aus der Paulskirche". In:
Germania_(Philipp_Veit)
Species of mammal
of Chicago Press. p. 339. ISBN 978-0-226-43722-4. Prothero, Donald R.; Schoch, Robert M. (2002). Horns, tusks, and flippers: the evolution of hoofed mammals
Okapi
Argentine footballer (born 1992)
world?". 3 Added Minutes. Retrieved 1 September 2025. Vollmer, Silvan; Schoch, David; Brandes, Ulrik (9 December 2024). "Penalty shoot-outs are tough
Emiliano_Martínez
1845 German children's book by Heinrich Hoffmann
Ramon; Bygum, Anette; Serre, Guy; Blume-Peytavi, Ulrike; Sprecher, Eli; Schoch, Susanne; Oji, Vinzenz; Hamm, Henning; Farrant, Paul; Simon, Michel; Betz
Struwwelpeter
Set of ten wooden weapons from the Palaeolithic Age
807T. doi:10.1038/385807a0. ISSN 1476-4687. PMID 9039910. S2CID 4283393. Schoch, Werner H.; Bigga, Gerlinde; Böhner, Utz; Richter, Pascale; Terberger, Thomas
Schöningen_spears
its changes during the ontogeny of the animal is published by Witzmann & Schoch (2026). Kear et al. (2026) revise the fossil material attributed to Erythrobatrachus
2026_in_paleontology
Species of freshwater bird
Loons". Adirondack Center for Loon Conservation. Retrieved 7 March 2022. Schoch, Nina; Glennon, Michale J.; Evers, David C.; Duron, Melissa; Jackson, Allyson
Common_loon
Chemical compound
1039/B110549N. PMID 12828371. Schmid, H. C.; Rassadina, V.; Oster, U.; Schoch, S.; Rüdiger, W. (2002). "Pre-Loading of Chlorophyll Synthase with Tetraprenyl
Chlorophyll_a
American composer and lyricist (1930–2021)
Games of the Broadway Legend. Bloomsbury Academic. ISBN 978-1493085835. Schoch, Richard (2024). How Sondheim Can Change Your Life. Ebury Press. ISBN 978-1-5299-4790-8
Stephen_Sondheim
American author and journalist (born 1955)
and Licensed Journalism]". California Monthly (Interview). Interviewed by Schoch, Russell. January 4, 2004. Retrieved June 16, 2026 – via TomDispatch. Oatman
Michael_Pollan
Extinct species of human
172 (2): 277–278. doi:10.1080/00665983.2015.1008839. hdl:10141/622351. Schoch, Werner H.; Bigga, Gerlinde; Böhner, Utz; Richter, Pascale; Terberger, Thomas
Neanderthal
Species of reptile
Tetrapods. Cambridge University Press. ISBN 978-0-521-45242-7. Sues HD, Schoch RR (7 November 2023). "The oldest known rhynchocephalian reptile from the
Tuatara
Ongoing extinction event caused by human activity
doi:10.2305/IUCN.UK.2016-3.RLTS.T22706052A94048187.en. McKinney, Michael L.; Schoch, Robert; Yonavjak, Logan (2013). "Conserving Biological Resources". Environmental
Holocene_extinction
Welsh actor (1925–1984)
442; Morley 2010, p. 494. Croall 2000, pp. 441–442. Croall 2000, p. 444; Schoch & Williams 2011, p. 59. Croall 2000, p. 443. Alpert 1986, p. 146; Bragg
Richard_Burton
2025 Swiss drama film
Nicole Bachmann as Dr. Strobel Doris Schefer as Pascale Schneider Margherita Schoch as Mrs. Kuhn Lale Yavaş as Patient Pema Shitsetsang as Doctor Volpe was
Late_Shift_(film)
Tragedy by William Shakespeare
232–233. Morrison 2002, pp. 235–237. Winter 1875. Morrison 2002, p. 241. Schoch 2002, pp. 58–75. Shaw 1961, p. 81. Moody 2002, p. 54. O'Connor 2002, p. 77
Hamlet
Clade of the first four-limbed vertebrates and their descendants
and Coates (2007), Coates et al (2008), Sigurdsen and Green (2011), and Schoch (2013, 2014). Cladogram modified after Coates, Ruta and Friedman (2008)
Tetrapod
System of glyphs from Easter Island
Retrieved from https://rapanuihistorian.substack.com/p/rongorongo-in-2023-pt-i Schoch & Melka (2020: 33) Adrienne Kaeppler (2001) "Rapa Nui Art and Aesthetics"
Rongorongo
Largest pyramid in the Giza Necropolis, Egypt
Rinaldi 1965a, p. 48. Lehner (1994). Notes and Photographs on the West-Schoch Sphinx Hypothesis. Petrie 1883, p. 84. Maragioglio & Rinaldi 1965a, p. 50
Great_Pyramid_of_Giza
Tragedy by William Shakespeare
365, 420. The Times 1845. Potter 2001, pp. 194–95. Levenson 2000, p. 84. Schoch 2002, pp. 62–63. Halio 1998, pp. 104–05. Winter 1893, pp. 46–47, 57. "Shakespeare
Romeo_and_Juliet
Indian Hindutva paramilitary organisation
India: Hindu Nationalism and the Rise of Ethnic Democracy. Translated by Schoch, Cynthia. Princeton University Press. p. 24. ISBN 9780691223094. Suresh
Rashtriya_Swayamsevak_Sangh
Play by William Shakespeare
126–127. Moody 2002, p. 38. Schoch 2002, pp. 58–59. Williams 2002, p. 128. Schoch 2002, pp. 61–62. Gay 2002, pp. 163–164. Schoch 2002, p. 64. Morrison 2002
Macbeth
Play by William Shakespeare
1972, p. 51. Foakes 1997, pp. 30–31. Schoch 2002, pp. 58–75. Potter 2001, p. 193. Jackson 1986, p. 206. Schoch 2002, p. 63. O'Connor 2002, p. 78. Wells
King_Lear
Traditional British puppet show
of Punch & Judy". Victoria and Albert Museum. Retrieved 2 February 2020. Schoch, Richard (2016). Writing the History of the British Stage 1660-1900. Cambridge
Punch_and_Judy
Professional theatre staged in London, England
Archived from the original on 31 December 2020. Retrieved 17 December 2020. Schoch, Richard (2016). Writing the History of the British Stage 1660-1900. Cambridge
West_End_theatre
Order of hoofed mammals
term had been used quite differently in the past. Also in 1984, Robert M. Schoch used the conceptually similar term Moropomorpha, which today applies synonymously
Perissodactyla
Genus of parasitic worms
arranged in three circles, one anterior circle followed by an unarmed region followed by two posteriorly circles instead of three circles of hooks evenly
Triaspiron
British writer and translator
(Hurst/OUP) (with Cynthia Schoch) 2018 – The Survival of the Jews in France, by Jacques Semelin (Hurst/OUP) (with Cynthia Schoch) 2018 – A Call for Revolution
Natasha_Lehrer
1497 engraving by Albrecht Dürer
in Context. Frankfurt: Städel Museum & Prestel, 2013. ISBN 3-7913-5317-9 Schoch, Rainer; Mende, Matthias; Scherbaum, Anna. Albrecht Dürer: Das druckgraphische
The_Four_Naked_Women_(Dürer)
US-based Christian movement
founded by Cannistraci, Gimenez, Green, Davis, Paul Paino, Thomas Reid, David Schoch, Dick Iverson, Bob Weiner, and John Meares. Other prominent ministers on
Apostolic-Prophetic_movement
College marching band in Austin, Texas
founded in 1900 by distinguished professor of chemistry, Dr. Eugene P. Schoch. The band is currently under the direction of Dr. Cliff Croomes. The band
University of Texas Longhorn Band
University_of_Texas_Longhorn_Band
Order of amphibians
Comparative Physiology. 176 (4): 575–586. doi:10.1007/BF00196422. S2CID 749622. Schoch, Rainer R. (19 March 2014). Amphibian Evolution: The Life of Early Land
Salamander
Major League Baseball franchise in Anaheim, California
Archived from the original on August 18, 2017. Retrieved May 30, 2017. Schoch, Josh (September 4, 2013). "Angels Will Finally Be Allowed to Drop Anaheim
Los_Angeles_Angels
Shield for the ventral and dorsal parts of turtles
Bibcode:2014NatCo...5.5211L. doi:10.1038/ncomms6211. ISSN 2041-1723. PMID 25376734. Schoch, Rainer R.; Sues, Hans-Dieter (2015). "A Middle Triassic stem-turtle and
Turtle_shell
Indian actor (born 1971)
Episodes Original airdate Dub airdate Notes The Young and the Restless N.P. Schoch J. Eddie Peck Cole Howard Hindi English 11000 26 March 1973 – present Batman
Chetanya_Adib
Four congruent circles associated with an arbelos
congruent circles associated with an arbelos. Introduced by Frank Power in the summer of 1998, each have the same area as Archimedes' twin circles, making
Archimedes'_quadruplets
Political and socioeconomic ideology
Series in Comparative Politics and International Studies. Translated by Schoch, Cynthia. New York: Columbia University Press. ISBN 978-0-231-14283-0. Johnson
Communism
Species of zebra
Taxonomy and Restoration of Quaggas". Kronos. 41 (1): 314–337. Prothero D.R; Schoch R. M (2003). Horns, Tusks, and Flippers: The Evolution of Hoofed Mammals'
Plains_zebra
Pantodont mammal genus from the Paleocene epoch
synonymized with Coryphodon anthracoideus by Lucas (1984) and Lucas and Schoch (1990); it was synonymized with Coryphodon radians by Uhen and Gingerich
Coryphodon
morphology and phylogenetic relationships of Neldasaurus is published by Schoch (2018). A study on the morphological changes in the skull that have been
2018 in amphibian paleontology
2018_in_amphibian_paleontology
American neuropsychiatrist
PMID 12526779. S2CID 7839933. Huang, Yan-You; Zakharenko, Stanislav S.; Schoch, Susanne; Kaeser, Pascal S.; Janz, Roger; Südhof, Thomas C.; Siegelbaum
Eric_Kandel
Convicted World War II war criminal (1899-1988)
Yeomans 2013, p. 22. Yeomans 2013, p. 194. Yeomans 2013, pp. 25–26. Jürgen Schoch: Der Deal mit dem kroatischen Faschisten – wie die Bundesanwaltschaft 1947
Andrija_Artuković
Cultural region in Southern Germany
Mineralogie, Geologie und Paläontologie. 1911 issue, 1911, pp. 78–83 Rainer R. Schoch: Comparative osteology of Mastodonsaurus giganteus (Jaeger, 1828) from the
Franconia
Armored vehicle with a crew-served weapon
Zaremba and Christina Sima, Hellgate Press, 2008 Convoy Conspiracy, Robert P. Schoch, Jr., Author House, 2012 The Hard Ride, Vietnam Gun Trucks, James Lyles
Gun_truck
Class of animals with milk-producing glands
2016-2.RLTS.T7121A22159785.en. Retrieved November 12, 2021. McKinney ML, Schoch R, Yonavjak L (2013). "Conserving Biological Resources". Environmental Science:
Mammal
in Comparative Politics and International Studies, translated by Cynthia Schoch, New York: Columbia University Press, ISBN 978-0-231-14283-0 Seybolt, Taylor
Mass killings under communist states
Mass_killings_under_communist_states
Christian Pentecostal movement
Kevin Conner, Dick Benjamin, Leonard Fox, Violet Kitely, Reg Lazelle, David Schoch, George Evans, Charlotte Baker, Fuchsia Pickett, Jim Watt and others, were
Latter Rain (post–World War II movement)
Latter_Rain_(post–World_War_II_movement)
Chemical element with atomic number 82 (Pb)
5 March 2024. Retrieved 27 May 2024. Marino et al. 1990, pp. 1183–1185. Schoch 1996, p. 111. "Leaded Aviation Fuel and the Environment | Federal Aviation
Lead
City in California, United States
"PCAD – Bixby Hotel, Waterfront, Long Beach, CA". pcad.lib.washington.edu. Schoch, Deborah (June 30, 2008). "Long Beach at sea over breakwater removal plan"
Long_Beach,_California
Edwin F. Schoch), made its only flight. After launching from a trapeze suspended below Boeing EB-29B Superfortress 44-84111 named "Monstro", Schoch was unable
List of accidents and incidents involving military aircraft (1945–1949)
List_of_accidents_and_incidents_involving_military_aircraft_(1945–1949)
Genus of worms
anterior trunk has 16-17 circles of spines and 4 circles of proboscis hooks with anterior two circles larger than posterior two circles; and a spineless space
Raosentis
Inverse sum of distances in a graph
2 (3): 416–418. doi:10.1017/nws.2014.25. ISSN 2050-1242. S2CID 3841410. Schoch, David; Valente, Thomas W.; Brandes, Ulrik (2017). "Correlations among centrality
Closeness_centrality
Collegiate summer baseball team in Massachusetts
Sammons 2003 Dane Sardinha 1999 Tim Scannell 1990 Casey Schmitt 2019 Stephen Schoch 2017–2018 Max Schrock 2013 Mike Schultz 1999 Victor Scott II 2022 J. B.
Cotuit_Kettleers
Phylum of protozoans
tb00030.x. PMID 9809012. S2CID 6557779. Adl SM, Bass D, Lane CE, Lukeš J, Schoch CL, Smirnov A, Agatha S, Berney C, Brown MW, Burki F, Cárdenas P, Čepička
Amoebozoa
Genus of worms
There are no known aberrant human infections for Pallisentis species. Schoch, Conrad L; Ciufo, Stacy; Domrachev, Mikhail; Hotton, Carol L; Kannan, Sivakumar;
Pallisentis
Genus of parasitic worms
the proboscis hooks in the anterior two circles are longer and stouter than the hooks in the posterior two circles and are separated from them by an unarmed
Pararaosentis
Extinct genus of temnospondyls
in the late Ladiunian. Separate evolution suggest separate stratigraphy. Schoch, Rainer R. (2019-05-24). "Osteology of the temnospondyl Trematosaurus brauni
Eocyclotosaurus
Phylum of single-celled organisms
described as Pseudophyllomitus (MAST-6). Adl SM, Bass D, Lane CE, Lukeš J, Schoch CL, Smirnov A, Agatha S, Berney C, Brown MW, Burki F, Cárdenas P, Čepička
Bigyra
College baseball team of the University of Virginia
advance to the Super Regionals. During this regional, Cavalier closer Stephen Schoch would go viral for his remarks during a post-game interview, being positively
Virginia_Cavaliers_baseball
Species of fungus
Reviews Microbiology. 2 (1): 43–56. doi:10.1038/nrmicro797. PMID 15035008. Schoch, Conrad L; Ciufo, Stacy; Domrachev, Mikhail; Hotton, Carol L; Kannan, Sivakumar;
Trichoderma_atroviride
Comparison of totalitarian ideologies
and Destroy: The Political Uses of Massacre and Genocide. Translated by Schoch, Cynthia. CERI Series in Comparative Politics and International Studies
Comparison of Nazism and Stalinism
Comparison_of_Nazism_and_Stalinism
Informal grouping of viruses
Mittelstaedt, Tobias; Bien, Christian G.; Drexler, Jan F.; Grote, Alexander; Schoch, Susanne; Becker, Albert J. (2010). "Presence of human herpes virus 6 DNA
Human_herpesvirus_6
Cellular appendage functioning as locomotive or sensory organelle
; Parfrey, Laura W.; Pawlowski, Jan; Rueckert, Sonja; Shadwick, Laura; Schoch, Conrad L.; Smirnov, Alexey; Spiegel, Frederick W. (September 2012). "The
Flagellum
British television presenter, broadcast journalist, trained actor, and singer
also featured in the book "The Pyramid Quest" written by Dr. Robert M. Schoch. Martyn then moved to New York City in 2004 to head up the award-winning
Martyn_Andrews
German scholar of Romance studies and literature
Rita Schober (1918-2012)". Verein romanistik.de e.V.). Prof. Dr. Christof Schöch (Universität Trier) i.A. Deutscher Romanistenverband. Retrieved 23 October
Rita_Schober
1506 painting by Albrecht Dürer
Stuttgart: Electa/Klett-Cotta. pp. 132–138. ISBN 3-88448-007-3. Rainer Schoch (1986). "Catalogue 124: Albrecht Dürer, The Hands of the Twelve-Year-Old
Christ Among the Doctors (Dürer)
Christ_Among_the_Doctors_(Dürer)
Common ancestor evolutionary evidence
doi:10.1144/GSL.SP.2006.258.01.10. S2CID 129493664. Prothero, Donald R.; Schoch, Robert M. (2002). Horns, tusks, and flippers: the evolution of hoofed mammals
Evidence_of_common_descent
Any life form too small for the naked human eye to see that lives in a marine environment
Viruses With Weird DNA Were Just Discovered in The Ocean". Sciencealert. Schoch CL, et al. (2020). "Autolykiviridae". NCBI Taxonomy: A Comprehensive Update
Marine_microorganisms
Study of lichen taxonomy and evolution
191 (1): 288–300. doi:10.1111/j.1469-8137.2011.03677.x. PMID 21434928. Schoch, Conrad L.; Seifert, Keith A.; Huhndorf, Sabine; Robert, Vincent; Spouge
Lichen_systematics
Church cantata by Johann Sebastian Bach
Bach's autograph score, there are original performing parts copied by Bach's circle. Bach structured the cantata in six movements and scored it intimately,
Tue Rechnung! Donnerwort, BWV 168
Tue_Rechnung!_Donnerwort,_BWV_168
Tie-breaking method in association football
Science. 58 (8): 1585–1591. doi:10.1287/mnsc.1120.1516. Vollmer, Silvan; Schoch, David; Brandes, Ulrik (9 December 2024). "Penalty shoot-outs are tough
Penalty shoot-out (association football)
Penalty_shoot-out_(association_football)
British costume designer and wigmaker
History. 40 (3): 597–618. doi:10.1353/jsh.2007.0056. S2CID 145115321. R. Schoch (28 January 2004). Queen Victoria and the Theatre of Her Age. Palgrave Macmillan
Willy_Clarkson
genocide the multiple forms of rescue. Translated by Emma Bentley; Cynthia Schoch. New York: Columbia University Press. p. 45. ISBN 978-0-231-80046-4. Üngör
Witnesses and testimonies of the Armenian genocide
Witnesses_and_testimonies_of_the_Armenian_genocide
American College President and administrator
president Dale Lick resigns". Tampa Bay Times. Retrieved July 30, 2023. Schoch, Al. "Florida State president resigns". United Press International. Retrieved
Dale_W._Lick
Series in Comparative Politics and International Studies. Translated by Schoch, Cynthia. New York: Columbia University Press. p. 331. ISBN 978-0-231-14283-0
Criticism_of_communist_states
International snowboarding competition
Simon Schoch (SUI) 2005 Whistler Jasey-Jay Anderson (CAN) Nicolas Huet (FRA) Siegfried Grabner (AUT) 2007 Arosa Simon Schoch (SUI) Philipp Schoch (SUI)
FIS Snowboard World Championships
FIS_Snowboard_World_Championships
Eastern Michigan University. August 31, 2009. Retrieved July 5, 2022. Schoch, Matt (November 6, 2019). "Bears' top wide receiver Allen Robinson still
List_of_people_from_Detroit
Reform model for urban residential development
the sidewalk and was designed by the architects Rudolf Klophaus, August Schoch and Erich zu Putlitz as a one-kitchen house. However, the owner C. Hinrichsen
Single-kitchen_home
Extinct genus of temnospondyls
doi:10.1002/ar.23582. PMID 28220619. Fröbisch, Nadia B.; Olori, Jennifer C.; Schoch, Rainer R.; Witzmann, Florian (2010-06-01). "Amphibian development in the
Cochleosaurus
May 1990 Severino Bernardini Fausto Bonzi Lucio Fregona 1991 John Lenihan Marius Hasler Woody Schoch 1992 Martin Jones Renatus Birrer Robin Bergstrand
World Mountain Running Championships
World_Mountain_Running_Championships
American nonprofit organization
Resumes Killing Wild Goats". Los Angeles Times. Retrieved 27 February 2011. Schoch, Deborah (12 November 2003). "Island Bison Ship Out for Plains". Los Angeles
In_Defense_of_Animals
data from the fossil record of larvae of temnospondyls, is published by Schoch & Witzmann (2024). A study on changes of the diversity of the temnospondyls
2024_in_paleontology
Genus of parasitic worms
consists of a proboscis covered in hooks arranged in three circles with six hooks in each circle, a proboscis receptacle, and a trunk. It is distinguished
Caballerorhynchus
Phylum of aquatic bacteria
Diversity". Nucleic Acids Research. 53: D1–D12. doi:10.1093/nar/gkaf1110. Schoch CL; et al. "Planctomycetota". National Center for Biotechnology Information
Planctomycetota
Nepali American educator, artist, and author (born 1945)
Ten Mysteries of the Deep", Ancient Aliens, Giorgio A. Tsoukalos, Robert Schoch, Hugh Newman, retrieved 2025-09-04 "Edgar Cayce: The Sleeping Prophet",
Deepak_Shimkhada
Rail line
of the railway was made between three Austrian companies called Gfrerer, Schoch, and Grossmann under the ordinance number 24089 from 15 March 1899 issued
Transylvanian_mining_railway
2008. Smith, Frank Barry. "About Veterans for Peace: Remembrance of Nikko Schoch". Archived from the original on 12 February 2008. Retrieved 23 February
Baháʼí_Faith_in_Vietnam
information on the anatomy of Mastodonsaurus cappelensis is presented by Schoch et al. (2023), who report the presence of anatomical differences between
2023_in_paleontology
American college basketball season
November 18, 2018 – ESPN". ESPN.com. Retrieved November 27, 2018. Matt Schoch. "Michigan State buries Tennessee Tech". South Bend Tribune. Associated
2018–19 Michigan State Spartans men's basketball team
2018–19_Michigan_State_Spartans_men's_basketball_team
SCHOCH CIRCLES
SCHOCH CIRCLES
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