How do you DERIVE the BELL CURVE? Mathoma 2017-06-11 | In this video, I'll derive the formula for the normal/Gaussian distribution. This argument is adapted from the work of the astronomer John Herschel in 1850 and the physicist James Clerk Maxwell in 1860. A similar argument is presented in this video: youtube.com/watch?v=ebewBjZmZTw&t=224sReferences / Further Reading:1. The Evolution of the Normal Distribution: http://www.ww.ingeniousmathstat.org/sites/default/files/pdf/upload_library/22/Allendoerfer/stahl96.pdf2. The Central Gaussian, or Normal, Distribution: http://www-biba.inrialpes.fr/Jaynes/cc07s.pdf3. J.C. Maxwell "Illustrations of the Dynamical Theory of Gases" (p. 152-154): http://hermes.ffn.ub.es/luisnavarro/nuevo_maletin/Maxwell_1860_Equilibrium_distribution.pdf4. en.wikipedia.org/wiki/Gaussian_integral5. en.wikipedia.org/wiki/Functional_equationErratum:32:35 - the left-hand side should be positive, not negative.
Lecture 1 on Aristotles Physics by Duane H. Berquist Mathoma 2022-10-23 | References:at-studies.com/welcome/texts-and-recordings/duane-berquist/school-aristotle/159/school-aristotleWilliam Wallace OP on Introductory Philosophy of Nature:youtube.com/playlist?list=PL6cPgDv4oMrsFHf7_MaZeXyuQpo5gfgHY
Pythagorean Theorem Converse: Euclids Elements - Book 1, Proposition 48 Mathoma 2021-04-11 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D48Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Pythagorean Theorem: Euclids Elements - Book 1, Proposition 47 Mathoma 2021-04-10 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D47Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 46 Mathoma 2021-04-10 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D46Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 45 Mathoma 2021-04-09 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D45Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 44 Mathoma 2021-04-09 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D44Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 43 Mathoma 2021-03-26 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D43Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 42 Mathoma 2021-03-25 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D42Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 41 Mathoma 2021-03-25 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D41Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 40 Mathoma 2021-03-25 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D40Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 39 Mathoma 2021-03-21 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D39Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 38 Mathoma 2021-03-20 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D38Greek-English parallel text plus diagrams:archive.org/details/JL_Heiberg___EUCLIDS_ELEMENTS_OF_GEOMETRYThis series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 37 Mathoma 2021-03-20 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D37This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 36 Mathoma 2021-03-19 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D36This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 35 Mathoma 2021-03-18 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D35This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 34 Mathoma 2021-03-18 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D34This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 33 Mathoma 2021-03-17 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D33This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 32 Mathoma 2021-03-17 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D32This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 31 Mathoma 2021-03-16 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D31This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 30 Mathoma 2021-03-16 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D30This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 29 Mathoma 2021-03-15 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D29This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 28 Mathoma 2021-03-15 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D28This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 27 Mathoma 2021-03-15 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D27This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 26 Mathoma 2021-03-14 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D26This series is part of a larger project, part of which covers geometry
Euclids Elements - Book 1, Proposition 25 Mathoma 2021-03-14 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D25This series is part of a larger project, part of which covers geometry
Euclids Elements - Book 1, Proposition 24 Mathoma 2021-03-13 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D24This series is part of a larger project, part of which covers geometry
Euclids Elements - Book 1, Proposition 23 Mathoma 2021-03-13 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D23This series is part of a larger project, part of which covers geometry
Euclids Elements - Book 1, Proposition 22 Mathoma 2021-03-13 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D22This series is part of a larger project, part of which covers geometry
Euclids Elements - Book 1, Proposition 21 Mathoma 2021-03-12 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D21This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 20 Mathoma 2021-03-12 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D20This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 19 Mathoma 2021-03-12 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D19This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 18 Mathoma 2021-03-12 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D18This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 17 Mathoma 2021-03-11 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D17This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 16 Mathoma 2021-03-11 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D16This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 15 Mathoma 2021-03-11 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D15This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 14 Mathoma 2021-03-10 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D14This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 13 Mathoma 2021-03-10 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D13This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 12 Mathoma 2021-03-09 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D12This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 11 Mathoma 2021-03-09 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D11This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 10 Mathoma 2021-03-08 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D10This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 9 Mathoma 2021-03-08 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D9This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 8 Mathoma 2021-03-08 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D8This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 7 Mathoma 2021-03-08 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D7This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 6 Mathoma 2021-03-06 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D6This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 5 (Pons Asinorum) Mathoma 2021-03-06 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D5This series is part of a larger project, part of which covers geometry.Errata:Angles are subtended by the relevant line segments, not 'subtend' the line segments.
Euclids Elements - Book 1, Proposition 4 Mathoma 2021-02-06 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D4This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 3 Mathoma 2021-02-06 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D3This series is part of a larger project, part of which covers geometry.
Euclids Elements - Book 1, Proposition 2 Mathoma 2021-02-04 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0086%3Abook%3D1%3Atype%3DProp%3Anumber%3D2This series is part of a larger project, part of which covers geometry.
Equilateral Triangle CONSTRUCTED with Ruler and Compass Mathoma 2021-02-03 | patreon.com/MathomaHeath's translation of Euclid's "Elements"http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.01.0086:id=elem.1.c.n.1This series is part of a larger project, part of which covers geometry.
The Authoritative Weight of Non-Definitive Magisterial Teaching by Lawrence Jerome King (Part 3) Mathoma 2020-12-02 | A guest reading by Riverrun.Text: cuislandora.wrlc.org/islandora/object/cuislandora%3A40891/datastream/PDF/view
