Uploaded January 2026 | Updated September 2026, 2 weeks ago
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
scribd.com/document/492462245/Instruction-Manual-for-Compensating-Polar-Planimeter
https://americanhistory.si.edu/collections/object-groups/planimeters/polar-amsler
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
patents.google.com/patent/US2674042A/en?inventor=hermann+ott&oq=hermann+ott
patents.google.com/patent/US2834642A/en?inventor=hermann+ott&oq=hermann+ott
rechnerlexikon.de/artikel/Spezial:Patentpage&srch=Planimeter
collection.sciencemuseumgroup.org.uk/search/object_type/planimeter
https://persweb.wabash.edu/facstaff/footer/planimeter/HowPlanimetersWork.htm
archive.org/details/KeuffelEsserCompensatingPolarPlanimeters1963/page/n15/mode/2up
uraone.com/PlanimeterVault/Ott/Ott-Supplement1toList302.pdf
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
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
scribd.com/document/492462245/Instruction-Manual-for-Compensating-Polar-Planimeter
https://americanhistory.si.edu/collections/object-groups/planimeters/polar-amsler
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
patents.google.com/patent/US2674042A/en?inventor=hermann+ott&oq=hermann+ott
patents.google.com/patent/US2834642A/en?inventor=hermann+ott&oq=hermann+ott
rechnerlexikon.de/artikel/Spezial:Patentpage&srch=Planimeter
collection.sciencemuseumgroup.org.uk/search/object_type/planimeter
https://persweb.wabash.edu/facstaff/footer/planimeter/HowPlanimetersWork.htm
archive.org/details/KeuffelEsserCompensatingPolarPlanimeters1963/page/n15/mode/2up
uraone.com/PlanimeterVault/Ott/Ott-Supplement1toList302.pdf
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
