The Algebra of Coplanar Vectors And Trigonometry
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In our eReader you can find the full English version of the book. Read The Algebra of Coplanar Vectors And Trigonometry Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Algebra of Coplanar Vectors And Trigonometry
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. .
is convergent, still more is the general series convergent. If the chain stretched out to its full length, (that is, so that the links are all in the same line,) has a finite length, any coiling or folding must bring its ends nearer together.
Hence, if the scalar series, which we may call the r-series, is convergent for all values of r, so is also the general series, which we may call the (r, u) series.
More commonly however the r-series is convergent only when r is less (or not greater) th...an some fixed quantity k ; then the (r,u) series is certainly convergent when r is less (or not greater) than k, but it may be that when r = k, the (r, u) series is convergent, though the r-series is not so. We shall also show (what is not in itself obvious) that it is divergent, when r is greater than k.
It would seem that this last assertion is not necessarily true, when the coefficients are complex. Though the regular coiling (due to the versors, ■*'*, i 2u , ifec.) may not bring the ends of the infinite chain to a finite distance from one another, it is con- ceivable that some farther folding (due to the versors i% i™-..-) might do so.
What to read after The Algebra of Coplanar Vectors And Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by R Baldwin Robert Baldwin Hayward to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. .
is convergent, still more is the general series convergent. If the chain stretched out to its full length, (that is, so that the links are all in the same line,) has a finite length, any coiling or folding must bring its ends nearer together.
Hence, if the scalar series, which we may call the r-series, is convergent for all values of r, so is also the general series, which we may call the (r, u) series.
More commonly however the r-series is convergent only when r is less (or not greater) th...an some fixed quantity k ; then the (r,u) series is certainly convergent when r is less (or not greater) than k, but it may be that when r = k, the (r, u) series is convergent, though the r-series is not so. We shall also show (what is not in itself obvious) that it is divergent, when r is greater than k.
It would seem that this last assertion is not necessarily true, when the coefficients are complex. Though the regular coiling (due to the versors, ■*'*, i 2u , ifec.) may not bring the ends of the infinite chain to a finite distance from one another, it is con- ceivable that some farther folding (due to the versors i% i™-..-) might do so.
What to read after The Algebra of Coplanar Vectors And Trigonometry?
You can find similar books in the "Read Also" column, or choose other free books by R Baldwin Robert Baldwin Hayward to read onlineMoreLess
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