File:GR QQ0 dia.png
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Summary edit
DescriptionGR QQ0 dia.png |
English: Square containing square with areas in golden ratio (inferior)
Deutsch: Quadrat, das ein Quadrat enthält, dessen Fläche im Golden Verhältnis steht (kleine Variante) |
Date | |
Source | Own work |
Author | Hans G. Oberlack |
Task edit
Given is a square of side length . Inserted is a second square of side length . What is the length of that leads to a golden ratio of the areas of the second square and the remaining area within the larger square?
General solution edit
If there a two areas and then they fulfill the golden ratio if:
What is the size of relative to ?
Starting with: we derive
, by replacing
, binomial formula
, rearranging
, rearranging
, binomial formula
, rearranging
, rearranging
, drawing the root
, rearranging
, since by definition
Specific solution edit
In the case of two squares and we have: and
, filling in the general solution
, using only the non-complex root
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 20:26, 28 April 2023 | 1,581 × 1,816 (21 KB) | Hans G. Oberlack (talk | contribs) | numbering adjusted | |
21:49, 27 April 2023 | 1,581 × 1,816 (21 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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Horizontal resolution | 129.92 dpc |
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Vertical resolution | 129.92 dpc |