Measuring Area without Integrating

For our art project related to art history. Ross and I are researching the history of the planimeter. 

We decided that Ross will attempt to create a polar planimeter whilst I try to create the hatchet variant. Admittedly the hatchet planimeter is quite simple in design and as such, I will also be helping Ross ideate some of the mechanisms for his portion.

 Alternatively, a more specialist type of planimeter we would be interested in recreating would be the Adisco Area Measurer (Area Meter). This one is more approachable for secondary students as this one approximates areas with curved rectangles, similar to a Riemann sum, while the other ones utilize Stokes' theorem.

Here are some of the sources I've used:

Eckel, L. H. (1953). The hatchet planimeter. The Forestry Chronicle, 29(3), 273–277. https://doi.org/10.5558/tfc29273-3

Foote, R. L., & Sandifer, E. (2004, January). Area Without Integration: Make Your Own Planimeter. https://persweb.wabash.edu/facstaff/footer/papers/foote.sandifer.reprint.pdf

Green, D. R. (2025, January 15). The hatchet planimeter. Uraone.Com. https://www.uraone.com/PlanimeterVault/hatchet/

How planimeters work. (n.d.). Retrieved December 5, 2025, from https://persweb.wabash.edu/facstaff/footer/planimeter/HowPlanimetersWork.htm

Powerhouse Collection—Adisco area measurer. (n.d.). Retrieved December 5, 2025, from https://collection.powerhouse.com.au/object/383315

Prytz planimeters. (n.d.). Retrieved December 5, 2025, from https://persweb.wabash.edu/facstaff/footer/planimeter/Prytz/Prytz.htm

Staecker, C. (2022, November 22). Lost area-measuring tool. YouTube. https://www.youtube.com/watch?si=JYlrmUObsW5hj-5R&v=xSgf_wxJIlk&feature=youtu.be

Tinker projects. (n.d.). Retrieved December 5, 2025, from https://tinkerprojects.angelfire.com/planimeter.html