Unsolved problems in geometry:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York u.a.
Springer
1994
|
| Edition: | 2. corr. print. |
| Series: | Unsolved problems in intuitive mathematics
2. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturangaben |
| Physical Description: | XV, 198 S. graph. Darst. |
| ISBN: | 0387975063 3540975063 |
Staff View
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| 100 | 1 | |a Croft, Hallard T. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Unsolved problems in geometry |c Hallard T. Croft ; Kenneth J. Falconer ; Richard K. Guy |
| 250 | |a 2. corr. print. | ||
| 264 | 1 | |a New York u.a. |b Springer |c 1994 | |
| 300 | |a XV, 198 S. |b graph. Darst. | ||
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| 490 | 1 | |a Unsolved problems in intuitive mathematics |v 2. | |
| 490 | 0 | |a Problem books in mathematics | |
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Record in the Search Index
| _version_ | 1804124811917524992 |
|---|---|
| adam_text | HALLARD T. CROFT KENNETH J. FALCONER
RICHARD K. GUY
UNSOLVED PROBLEM
S
IN GEOMETR
Y
WITH 66 FIGURES
SPRINGER-VERLAG
NEW YORK BERLIN HEIDELBERG LONDON
PARIS TOKYO HONG KONG BARCELONA
YY ;YY
PREFACE
OTHE
R PROBLE
M COLLECTIONS
STANDAR
D REFERENCES
NOTATIO
N AN
D DEFINITIONS
SETS. 1 GEOMETRICAL TRANSFORMATIONS
. 3 LENGTH, AREA, AN
D VOLUME. 4
A. CONVEXITY
AI
. TH
E EQUICHORDA
L POIN
T PROBLEM
. 9 A2
. HAMMER
S X-RAY PROBLEMS
. 11
A3
. CONCURREN
T NORMALS
. 14 A4
. BILLIARD BALL TRAJECTORIES IN CONVEX
REGIONS. 15 A5
. ILLUMINATIO
N PROBLEMS
. 18 A6
. TH
E FLOATING BODY
PROBLEM. 19 A7
. DIVISION OF CONVEX BODIES BY LINES OR PLANES THROUG
H A
POINT
. 20 A8
. SECTIONS THROUG
H TH
E CENTROI
D OF A CONVEX BODY
. 21
A9
. SECTIONS OF CENTRO-SYMMETRIC CONVEX BODIES. 22 A10
. WHA
T CAN YOU
TEIL ABOU
T A CONVEX BOD
Y FROM ITS SHADOWS? 23 ALL
. WHA
T CAN YOU TEIL
ABOU
T A CONVEX BODY FROM ITS SECTIONS? 24 A12
. OVERLAPPIN
G CONVEX
BODIES. 25 A13
. INTERSECTION
S OF CONGRUEN
T SURFACES. 26 A14
. ROTATIN
G
POLYHEDRA. 26 A15
. INSCRIBED AN
D CIRCUMSCRIBED CENTRO-SYMMETRIC
BODIES. 21 A16
. INSCRIBED AFFINE COPIES OF CONVEX BODIES. 28
AI7
. ISOPERIMETRI
C INEQUALITIES AN
D EXTREMAL PROBLEMS
. 28 AI8
. VOLUME
AGAINST WIDTH. 29 A19
. EXTREMAL PROBLEM
S FOR ELONGATE
D SETS. 30
A20
. DIDO
S PROBLEM
. 30 A21
. BLASCHKE S PROBLEM
. 32 A22
. MINIMA
L
BODIES OF CONSTAN
T WIDTH. 34 A23
. CONSTRAINE
D ISOPERIMETRIC
PROBLEMS. 34 A24
. IS A BODY FAIRLY ROUN
D IF ALL ITS SECTIONS ARE? 35
A25
. HOW FAR APAR
T CAN VARIOUS CENTERS BE? 36 A26
. DIVIDING U
P A PIECE
OF LAND BY A SHOR
T FENCE. 37 ALL. MIDPOINT
S OF DIAMETERS OF SETS OF
CONSTANT WIDTH. 38 A28
. LARGEST CONVEX HUELL OF A
N AR
C OF A GIVEN
LENGTH. 38 A29
. ROAD
S ON PLANETS
. 39 A30
. TH
E SHORTEST CURVE CUTTIN
G
ALL THE LINES THROUG
H A DISK. 39 A31
. CONE
S BASED ON CONVEX SETS. 41
A32
. GENERALIZED ELLIPSES. 42 A33
. CONI
C SECTIONS THROUG
H FIVE
POINTS. 43 A34
. TH
E SHAP
E OF WOR
N STONES. 43 A35
. GEODESICS. 44
A36. CONVEX SETS WITH UNIVERSAL SECTIONS. 45 A37
. CONVEX SPACE-FILLING
CURVES. 46 A38
. M-CONVEX SETS. 46
B. POLYGONS, POLYHEDRA
, AN
D POLYTOPE
S
BL
. FITTING ON
E TRIANGLE INSIDE ANOTHER
. 50 B2
. INSCRIBING POLYGONS IN
CURVES. 51 B3
. MAXIMA
L REGULAE
R POLYHEDR
A INSCRIBED IN REGULAE
R
POLYHEDRA. 52 B4
. PRINC
E RUPERT
S PROBLEM
. 53 B5
. RANDO
M POLYGONS
AND POLYHEDRA
. 54 B6
. EXTREMA
L PROBLEM
S FOR POLYGONS
. 57 B7
. LONGEST
CHORDS OF POLYGONS. 58 B8
. ISOPERIMETRI
C INEQUALITIES FOR POLYHEDRA
. 58
B9
. INEQUALITIES FOR SUMS OF EDGE LENGTHS OF POLYHEDRA
. 59
BIO. SHADOWS OF POLYHEDRA
. 60 BLL
. DIHEDRA
L ANGLES OF POLYHEDRA
. 61
B12
. MONOSTATI
C POLYHEDRA
. 61 B13
. RIGIDITY OF POLYHEDRA
. 61
B14
. RIGIDITY OF FRAMEWORKS. 63 B15
. COUNTIN
G POLYHEDRA
. 65 B16
. TH
E
SIZES OF TH
E FACES OF A POLYHEDRON
. 68 B17
. UNIMODALIT
Y OF/-VECTOR
S OF
POLYTOPES. 69 B18
. INSCRIBABL
E AN
D CIRCUMSCRIBABLE POLYHEDRA
. 70
B19
. TRUNCATIN
G POLYHEDRA
. 72 B20
. LENGTHS OF PATH
S ON POLYHEDRA. 72
B21
. NET
S OF POLYHEDRA
. 73 B22
. POLYHEDR
A WITH CONGRUEN
T FACES. 75
B23
. ORDERIN
G THE FACES OF A POLYHEDRON
. 75 B24
. TH
E FOUR COLOR
CONJECTURE FOR TOROIDA
L POLYHEDRA
. 75 B25
. SEQUENCES OF POLYGON
S AN
D
POLYHEDRA. 76
C. TILING AN
D DISSECTION
CL
. CONWAY
S FRIED POTAT
O PROBLEM
. 80 C2
. SQUARIN
G TH
E SQUARE
. 81
C3
. MRS
. PERKINS
S QUILT. 83 C4
. DECOMPOSIN
G A SQUARE OR A CUBE INT
O N
SMALLER ONES. 85 C5
. TILING WITH INCOMPARABL
E RECTANGLES AN
D CUBOIDS. 85
C6
. CUTTIN
G U
P SQUARES, CIRCLES, AN
D POLYGONS. 87 C7
. DISSECTING A
POLYGON INT
O NEARL
Y EQUILATERA
L TRIANGLES. 89 C8
. DISSECTING TH
E SPHERE
INTO SMALL CONGRUEN
T PIECES. 90 C9
. TH
E SIMPLEXITY OF TH
E D-CUBE. 90
CIO. TILING THE PLAN
E WITH SQUARES. 91 CI
L TILING THE PLAN
E WITH
TRIANGLES. 92 C12
. ROTATIONA
L SYMMETRIES OF TILES. 93 C13
. TILINGS WITH A
CONSTANT NUMBER OF NEIGHBORS. 94 C14
. WHICH POLYGONS TILE THE PLANE? 95
C15. ISOPERIMETRIC PROBLEM
S FOR TILINGS. 96 C16
. POLYOMINOES
. 96
C17. REPTILES. 99 C18
. APERIODIC TILINGS. 101 C19
. DECOMPOSING A
SPHERE INTO CIRCULAR ARCS. 103 C20
. PROBLEMS IN EQUIDECOMPOSABILITY. 104
D
. PACKING AN
D COVERIN
G
D
L PACKING CIRCLES, O
R SPREADING POINTS
, IN A SQUARE. 108 D2
. SPREADIN
G
POINTS IN A CIRCLE. 110 D3
. COVERING A CIRCLE WITH EQUA
L DISKS. 111
D4
. PACKING EQUAL SQUARES IN A SQUARE
. 111 D5
. PACKIN
G UNEQUAL
THEOREM
. 121 D14
. BORSUK S CONJECTURE. 123 D15
. UNIVERSAL COVERS. 125
D16
. UNIVERSAL COVERS FOR SEVERAL SETS. 127 D17
. HADWIGER
S COVERING
CONJECTURE. 128 D18
. TH
E WORM PROBLEM
. 129
E. COMBINATORIA
L GEOMETR
Y 131
EL
. HELLY-TYPE PROBLEMS
. 131 E2
. VARIATION
S O
N KRASNOSEL SKII S
THEOREM
. 133 E3
. COMMO
N TRANSVERSALS. 135 E4
. VARIATION
S ON RADON
S
THEOREM
. 136 E5
. COLLECTIONS OF DISKS WITH N
O THRE
E IN A LINE. 137
E6
. MOVIN
G DISKS AROUND
. 138 E7
. NEIGHBORL
Y CONVEX BODIES. 139
E8
. SEPARATIN
G OBJECTS. 141 E9
. LATTICE POIN
T PROBLEMS
. 143 E10
. SETS
COVERING CONSTAN
T NUMBER
S OF LATTICE POINTS
. 143 ELL
. SETS THA
T CAN BE
MOVED T
O COVER SEVERAL LATTICE POINTS
. 144 E12
. SETS THA
T ALWAYS COVER
SEVERAL LATTICE POINTS
. 145 E13
. VARIATION
S ON MINKOWSKI
S THEOREM
. 146
E14
. POSITIONIN
G CONVEX SETS RELATIVE T
O DISCRETE SETS. 148
F
. FINIT
E SETS OF POINT
S 149
FL
. MINIMU
M NUMBE
R OF DISTINCT DISTANCES. 150 F2
. REPEATED DIS
TANCES. 151 F3
. TWO-DISTANCE SETS. 152 F4
. CA
N EACH DISTANCE OCCUR A
DIFFERENT NUMBE
R OF TIMES? 153 F5
. WELL-SPACED SETS OF POINTS
. 154
F6
. ISOSCELES TRIANGLES DETERMINED BY A SET OF POINTS
. 154 F7
. AREAS OF
TRIANGLES DETERMINED BY A SET OF POINTS
. 155 F8
. CONVEX POLYGONS
DETERMINE
D BY A SET OF POINTS
. 155 F9
. CIRCLES THROUG
H POIN
T SETS. 156
F10
. PERPENDICULA
R BISECTORS. 157 FLL
. SETS CUT OFF BY STRAIGH
T LINES. 757
F12
. LINES THROUG
H SETS OF POINTS
. 158 F13
. ANGLES DETERMINED BY A SET
OF POINTS
. 160 F14
. FURTHE
R PROBLEM
S IN DISCRETE GEOMETRY. 161
F15
. TH
E SHORTEST PAT
H JOININ
G A SET OF POINTS
. 162 F16
. CONNECTIN
G
POINT
S BY ARCS. 164 F17
. ARRANGIN
G POINT
S ON A SPHERE. 165
G. GENERA
L GEOMETRI
E PROBLEM
S 168
GL
. MAGIC NUMBERS
. 168 G2
. METRICALLY HOMOGENEOU
S SETS. 169
G3
. ARCS WITH INCREASING CHORDS
. 169 G4
. MAXIMA
L SETS AVOIDING CERTAIN
DISTANC
E CONFIGURATIONS. / 70 G5
. MOVIN
G FURNITURE AROUND
. 171
G6
. QUESTION
S RELATED T
O TH
E KAKEY
A PROBLEM
. 173 G7
. MEASURABL
E SETS
AN
D LINES. 175 G8
. DETERMININ
G CURVES FROM INTERSECTIONS WITH LINES. / 75
G9
. TW
O SETS WHICH ALWAYS INTERSECT IN A POINT
. 176 GIO. TH
E CHROMATI
C
NUMBE
R OF TH
E PLANE AN
D OF SPACE. 177 GH
. GEOMETRI
E GRAPHS
. 180
G12
. EUCLIDEAN RAMSEY PROBLEMS
. 181 G13
. TRIANGLES WITH VERTICES IN
SETS OF A GIVEN AREA. 182 G14
. SETS CONTAININ
G LARGE TRIANGLES. 182
G15
. SIMILAR COPIES OF SEQUENCES. 183 G16
. UNION
S OF SIMILAR COPIES OF
SETS. 184
INDEX OF AUTHOR
S CITED 185
GENERA
L INDE
X 195
YY
.
|
| any_adam_object | 1 |
| author | Croft, Hallard T. Falconer, Kenneth J. 1952- Guy, Richard K. 1916-2020 |
| author_GND | (DE-588)112970613 (DE-588)124655254 |
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| author_sort | Croft, Hallard T. |
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| bvnumber | BV010386432 |
| callnumber-first | Q - Science |
| callnumber-label | QA43 |
| callnumber-raw | QA43 |
| callnumber-search | QA43 |
| callnumber-sort | QA 243 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)31887603 (DE-599)BVBBV010386432 |
| dewey-full | 516 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry 510 - Mathematics |
| dewey-raw | 516 510 |
| dewey-search | 516 510 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2. corr. print. |
| format | Book |
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| id | DE-604.BV010386432 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:51:36Z |
| institution | BVB |
| isbn | 0387975063 3540975063 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006915720 |
| oclc_num | 31887603 |
| open_access_boolean | |
| owner | DE-29T DE-12 DE-703 DE-11 |
| owner_facet | DE-29T DE-12 DE-703 DE-11 |
| physical | XV, 198 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series | Unsolved problems in intuitive mathematics |
| series2 | Unsolved problems in intuitive mathematics Problem books in mathematics |
| spelling | Croft, Hallard T. Verfasser aut Unsolved problems in geometry Hallard T. Croft ; Kenneth J. Falconer ; Richard K. Guy 2. corr. print. New York u.a. Springer 1994 XV, 198 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Unsolved problems in intuitive mathematics 2. Problem books in mathematics Literaturangaben Geometry Geometrie (DE-588)4020236-7 gnd rswk-swf Ungelöstes Problem (DE-588)4186869-9 gnd rswk-swf Geometrie (DE-588)4020236-7 s Ungelöstes Problem (DE-588)4186869-9 s DE-604 Falconer, Kenneth J. 1952- Verfasser (DE-588)112970613 aut Guy, Richard K. 1916-2020 Verfasser (DE-588)124655254 aut Unsolved problems in intuitive mathematics 2. (DE-604)BV001894954 2 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006915720&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Croft, Hallard T. Falconer, Kenneth J. 1952- Guy, Richard K. 1916-2020 Unsolved problems in geometry Unsolved problems in intuitive mathematics Geometry Geometrie (DE-588)4020236-7 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4186869-9 |
| title | Unsolved problems in geometry |
| title_auth | Unsolved problems in geometry |
| title_exact_search | Unsolved problems in geometry |
| title_full | Unsolved problems in geometry Hallard T. Croft ; Kenneth J. Falconer ; Richard K. Guy |
| title_fullStr | Unsolved problems in geometry Hallard T. Croft ; Kenneth J. Falconer ; Richard K. Guy |
| title_full_unstemmed | Unsolved problems in geometry Hallard T. Croft ; Kenneth J. Falconer ; Richard K. Guy |
| title_short | Unsolved problems in geometry |
| title_sort | unsolved problems in geometry |
| topic | Geometry Geometrie (DE-588)4020236-7 gnd Ungelöstes Problem (DE-588)4186869-9 gnd |
| topic_facet | Geometry Geometrie Ungelöstes Problem |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006915720&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV001894954 |
| work_keys_str_mv | AT crofthallardt unsolvedproblemsingeometry AT falconerkennethj unsolvedproblemsingeometry AT guyrichardk unsolvedproblemsingeometry |