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/49246... https://americanhistory.si.edu/collec... https://chsi.emuseum.com/objects/1572... https://www.mathinstruments.ch/pdf/co... https://persweb.wabash.edu/facstaff/f... https://patents.google.com/patent/US2... https://patents.google.com/patent/US2... https://www.rechnerlexikon.de/artikel... https://collection.sciencemuseumgroup... https://persweb.wabash.edu/facstaff/f... https://archive.org/details/KeuffelEs... https://www.uraone.com/PlanimeterVaul... https://www.scribd.com/document/49246... http://www.mathinstruments.ch/pdf/ams... http://www.mathinstruments.ch/pdf/ams...
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