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In the following sentence:

It would mean that like the Greeks, the Egyptians began to see the importance of calculating the curved surfaces of solids like the sphere in terms of a rectangular or rectiplanar surfaces.

What does the term "rectiplanar surface" refer to? Is it perhaps just the old word for a rectilinear surface?

Michael Munta
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2 Answers2

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This extract from a US Patent offers an implicit definition:

In FIGS. 1-10, the panel filter element 38 is rectiplanar, i.e. lies in a single two-dimensional plane which is rectilinear in each of such two dimensions. In further embodiments, the panel filter element is non-rectiplanar, for example as shown in FIGS. 11-21, where like reference numerals are used from above where appropriate to facilitate understanding. In FIGS. 11-13, panel filter element 80 has at least one curved section 82,

https://patents.justia.com/patent/8668756

Ethan Bolker
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  • Where would I be able to see the referenced figures? – Michael Munta Sep 23 '21 at 16:38
  • @MichaelMunta The entire patent application is public. It may be available on the web. – Ethan Bolker Sep 23 '21 at 18:09
  • Hey, I found the pictures so I am wondering if you can explain how to understand this "rectiplanarity" in these images? Some images are obviously 3-d. https://pdfpiw.uspto.gov/.piw?PageNum=0&docid=08668756&IDKey=EBB97A352864&HomeUrl=http%3A%2F%2Fpatft.uspto.gov%2Fnetacgi%2Fnph-Parser%3FSect1%3DPTO2%2526Sect2%3DHITOFF%2526p%3D1%2526u%3D%25252Fnetahtml%25252FPTO%25252Fsearch-bool.html%2526r%3D1%2526f%3DG%2526l%3D50%2526co1%3DAND%2526d%3DPTXT%2526s1%3D20130199143%2526OS%3D20130199143%2526RS%3D20130199143. – Michael Munta Sep 24 '21 at 14:50
  • @MichaelMunta The patent is for a 3d object, but the explicit reference "panel filter element 38" is to a part that looks planar. – Ethan Bolker Sep 24 '21 at 15:24
  • Is it though? There are other pictures where only that element is shown and it looks 3d to me. Check figure 4 and 5. Want to understand it clearly before awarding the bounty. – Michael Munta Sep 25 '21 at 10:09
  • @MichaelMunta They look two dimensional to me. The view in Figure 4 might be isometric rather than perspective, which would distort the view. In Figure 5 I think you are looking at a side view of part 38, which is the planar top of what's shown. – Ethan Bolker Sep 25 '21 at 20:38
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Marshall Clagett, the author of your sentence, writes in his treatise on Archimedes:

...so there is no such ratio between a sphere and a "rectilinear" (i.e. rectiplanar) body...

(p. 226 of the 1987 edition). This doesn't answer your question in the general case, though.

K B Dave
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  • What do you mean in the general case? If the words indeed are interchangeable then it does refer to some sort of surface that is characterized by straight lines and right angles? – Michael Munta Sep 23 '21 at 16:23