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I am new to this Stack Exchange venue, so please don't shoot me if this question is not appropriate. This question was taken Math Stack Exchange.

In 2003, the Belgian plant biotechnologist Johan Gielis proposed a formula that allows for the description of a wide variety of shapes in \$2d\$, \$3d\$ and higher dimensions. This is the formula

$$r( \phi) = \bigg[\bigg|{\frac{\cos(m \phi/4) }{a} }\bigg|^{n_2} + \bigg| \frac{ \sin(m \phi / 4)}{b} \bigg|^{n_3} \bigg]^{-\frac{1}{n_1}} $$

in polar coordinates, where \$r\$ is the radius and \$\phi\$ is the angle. More information can be obtained via the wikipedia page. Gielis' original article can be viewed here.

A couple of days ago, it was reported by numerous dutch newspapers and magazines that this formula can be applied to make new WIFI antennas that supposedly are much more efficient than previous antennas. Furthermore, it is claimed by the Telegraaf newspaper that this formula can be used by architects to create \$3d\$ designs more easily and that it could be used to design software for $3d$ printers. (See the Telegraaf article here. It is in Dutch, but one could use google translate to understand it). In the online magazine called Kennislink, it is claimed that the formula can be used to reduce the size of \$3d\$-imageing software a thousandfold. (See the Kennislink article here.)

Questions: To what extent are these claims true? Why do you believe so?

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closed as primarily opinion-based by Dave Tweed, Daniel Grillo, Chetan Bhargava, Matt Young, embedded.kyle Feb 20 '14 at 21:40

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • \$\begingroup\$ A WiFi antenna can be up to 70% efficient meaning it might lose 3dB of power. Losses are usually due to the circuits and materials in close proximity to the antennas. So, say you can halve this loss with a new-fangled formula - that's a 1.5dB improvement - what will the regulatory bodies say? I'll tell you - they'll say "turn your power down by 1.5dB to stop cross interference". It's not going to be earth shattering good-news for the greens and tree huggers but it's one small step in the right direction I suppose. Hmmm, a formula that might save the planet? \$\endgroup\$ – Andy aka Feb 20 '14 at 22:15
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Well, there's absolutely no information as to how the improved antenna would be improved, or even what it would look like exactly, which makes it hard to say. It's generally hard to analyse complex antenna designs; maybe they have something there.

For the 3D design case, it is generally true that expressing something as a generated surface of a function is much more compact than decomposing it into polygons or pixels. So provided they have a good algorithm for inferring the curve that describes a particular shape, that part is very plausible... if you're making things that are that kind of shape. However, I don't think the file size is much of an issue in 3D printing.

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