Ott Compensating Planimeter: Hot Integrals in Your Area

Invented in the early 19th century, Planimeters are used to measure the area of irregular two-dimensional shapes such as regions on maps or cross-sections in engineering drawings. The mathematics behind their operation are extremely clever, relying on an elegant application of the Difference of Areas Theorem / Green's Theorem. 0:00 Intro 1:16 Early Planimeters 1:49 Hermann Planimeter 2:51 Rolling Sphere Planimeters 3:29 Ball-and-Disk Integrators 4:38 Amsler Planimeter 5:26 Ott Planimeter: Overview 7:06 Ott Planimeter: Use 7:34 Mathematical Principles 10:43 Ott Planimeter: Accessories 11:48 Other Planimeters 12:10 Outro SOURCES https://www.scribd.com/document/492462245/Instruction-Manual-for-Compensating-Polar-Planimeter https://americanhistory.si.edu/collections/object-groups/planimeters/polar-amsler https://chsi.emuseum.com/objects/15726/rolling-sphere-planimeter https://www.mathinstruments.ch/pdf/coradi_ca1930_rolling_sphere_planimeter.pdf https://persweb.wabash.edu/facstaff/footer/planimeter/PreAmsler.htm https://patents.google.com/patent/US2674042A/en?inventor=hermann+ott&oq=hermann+ott https://patents.google.com/patent/US2834642A/en?inventor=hermann+ott&oq=hermann+ott https://www.rechnerlexikon.de/artikel/Spezial:Patentpage&srch=Planimeter https://collection.sciencemuseumgroup.org.uk/search/object_type/planimeter https://persweb.wabash.edu/facstaff/footer/planimeter/HowPlanimetersWork.htm https://archive.org/details/KeuffelEsserCompensatingPolarPlanimeters1963/page/n15/mode/2up https://www.uraone.com/PlanimeterVault/Ott/Ott-Supplement1toList302.pdf https://www.scribd.com/document/492462245/Instruction-Manual-for-Compensating-Polar-Planimeter http://www.mathinstruments.ch/pdf/amsler_ca1928_instructions_for_amslers_planimeter.pdf http://www.mathinstruments.ch/pdf/amsler_ca1928_instructions_for_amslers_planimeter.pdf