File:GR QQ1 dia.png
![File:GR QQ1 dia.png](https://upload.wikimedia.org/wikipedia/commons/thumb/c/ca/GR_QQ1_dia.png/525px-GR_QQ1_dia.png?20230428224357)
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Captions
Captions
Summary
[edit]DescriptionGR QQ1 dia.png |
English: Square containing square with areas in golden ratio (superior)
Deutsch: Quadrat, das ein Quadrat enthält, dessen Fläche im Golden Verhältnis steht (große 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
, binomial formula
, rearranging
, drawing the root
, rearranging
, excluding the second term since
, rearranging
, rearranging
, rearranging
, rearranging
, rearranging
Specific solution
[edit]In the case of two squares and
we have:
and
, filling in the general solution
, using only the non-complex root
Licensing
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:43, 28 April 2023 | ![]() | 1,590 × 1,816 (23 KB) | Hans G. Oberlack (talk | contribs) | Uploaded own work with UploadWizard |
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Vertical resolution | 129.92 dpc |