| 1. |
Plane Curves, Polar Coordinates and Winding Numbers |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 75-91
BakerJohn A.,
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摘要:
This article begins with an elementary proof of (and motivation for) the fact that a plane curve can be suitably represented in polar coordinates. Our aim is to demonstrate that this fact can be used(i)to give natural definitions of“winding number”and“degree”(in two dimensions); and thereby(ii)to deduce, with relative ease, several important, well-known results from diverse areas of mathematics including real and complex analysis, algebra, plane topology and differential equations.Among these results are the fundamental theorem of algebra, Brouwer's Fixed Point Theorem in the plane, an open mapping theorem in two dimensions, and assertions concerning oscillation and stability of differential equations.
ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977580
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 2. |
Limerick |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 91-91
WhiteArthur,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977581
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 3. |
Packing a Box with Bricks |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 92-97
JepsenCharles H.,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977582
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 4. |
Proof without Words: sin(x+y) = sinxcosy+ cosxsinyforx+y<π |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 97-97
KungSidney H.,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977583
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 5. |
Complements of Linear Subspaces |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 98-103
TingleyDaryl,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977584
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 6. |
Proof without Words: The Sum of Odd Numbers |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 103-103
LehelJenő,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977585
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 7. |
Tetrahedral Numbers as Sums of Square Numbers |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 104-108
AlthoenS. C.,
LacampagneC. B.,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977586
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 8. |
Regular Polygons with Rational Area or Perimeter |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 109-114
KillgroveR. B.,
KosterD. W.,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977587
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 9. |
Proof without Words |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 114-114
LogothettiDave,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977588
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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| 10. |
Some Counting Problems Involving the Multinomial Expansion |
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Mathematics Magazine,
Volume 64,
Issue 2,
1991,
Page 115-122
DoddFred,
PeeleRhodes,
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ISSN:0025-570X
DOI:10.1080/0025570X.1991.11977589
出版商:Taylor&Francis
年代:1991
数据来源: Taylor
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