Overlapping circles: diam.fraction vs area fraction

lineup shared this question 6 years ago
Answered

The most common mistake during partial solar eclipses is to mismatch the magnitude of umbra as fraction of the eclipsed area referred to full solar disc. Instead, the magnitude defines the fraction of diameter.


The proposed problem is to compute the maximum discrepancy between both fractions, being known that the area fraction is always less. Thank you in advance.

https://ggbm.at/1388359a4ac034bd09b99b8bff11fdb8dbf48c6

Comments (2)

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Hi,


do you want something like that ?

https://ggbm.at/1388363

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Thank you for your quick answer.

My request is just a little bit different, please look at the figure coming from your sheet.

The determination of the point of maximum in your pink graph should be carried out using any method (also numerically as per the highest accuracy allowed by Geogebra, i.e. 15 decimal places) but with the final result appearing for example: x_max=0.2365... y_max=11.5421...%.72055db8376d4ee15bcc931ea685feb3

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