Maths for map makers:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Latheronwheel
Whittles
1997
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 305 S. graph. Darst. |
| ISBN: | 1870325915 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV012006044 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | t | ||
| 008 | 980616s1997 d||| |||| 00||| eng d | ||
| 020 | |a 1870325915 |9 1-870325-91-5 | ||
| 035 | |a (OCoLC)473723150 | ||
| 035 | |a (DE-599)BVBBV012006044 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-703 | ||
| 084 | |a RB 10103 |0 (DE-625)142220:12616 |2 rvk | ||
| 100 | 1 | |a Allan, Arthur L. |e Verfasser |0 (DE-588)142349453 |4 aut | |
| 245 | 1 | 0 | |a Maths for map makers |c by Arthur Allan |
| 264 | 1 | |a Latheronwheel |b Whittles |c 1997 | |
| 300 | |a XIII, 305 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Kartografie |0 (DE-588)4029823-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Mathematik |0 (DE-588)4037944-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kartografie |0 (DE-588)4029823-1 |D s |
| 689 | 0 | 1 | |a Mathematik |0 (DE-588)4037944-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 856 | 4 | 2 | |m GBV Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008124783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-008124783 | ||
Datensatz im Suchindex
| _version_ | 1804126601818931200 |
|---|---|
| adam_text | SUB GOTTINGEN 7 210 050 861 99 A 2003 MATHS FOR MAP MAKERS BY ARTHUR
ALLAN WHITTLES PUBLISHING /V CONTENTS CHAPTER 1 NUMBERS AND CALCULATION
1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14 1.15 1.16
1.17 1.18 1.19 1.20 1.21 1.22 1.23 1.24 1.25 1.26 TER2 2.1 2.2 2.3 THE
LANGUAGE OF MATHEMATICS NUMBERS AND YOUR CALCULATOR NUMBERS IN EXPONENT
FORM INTEGERS: SEQUENCE AND SERIES REAL OR DECIMAL NUMBERS SIGNIFICANT
FIGURES TRUNCATED AND ROUNDED NUMBERS OPERATORS AND STORES RECIPROCALS
POWERS FACTORIALS INDICES IN MULTIPLICATION INDICES IN DIVISION
LOGARITHMS THE BASE OF NATURAL LOGARITHMS E DIVISION USING LOGARITHMS
POWERS BY LOGARITHMS ARITHMETIC PROGRESSION POLYNOMIALS SUM OF THE
SQUARES OF THE FIRST N INTEGERS RATIOS INEQUALITIES THE BINOMIAL THEOREM
PASCAL S TRIANGLE GENERAL CASE OF BINOMIAL THEOREM SPECIAL CASE OF
BINOMIAL SERIES PLANE GEOMETRY PLANES AND STRAIGHT LINES STRAIGHT LINES
INTERSECTING, NORMAL AND PARALLEL LINES 1 2 4 5 6 6 7 7 8 8 10 10 10 11
12 13 13 14 15 16 18 19 20 21 22 22 25 25 27 27 VI/ MATHS FOR MAP MAKERS
2.4 REFERENCE GRID 28 2.5 PARALLELOGRAM, RECTANGLE, SQUARE AND RHOMBUS
30 2.6 PYTHAGORAS S THEOREM FOR A RIGHT ANGLED TRIANGLE 30 2.7- PROOF OF
PYTHAGORAS S THEOREM 31 2.8 THE CIRCLE 32 2.9 ANGLES 35 2.10 SEXAGESIMAL
SYSTEM 36 2.11 SEXAGESIMAL TIME SYSTEM 36 2.12 CENTESIMAL SYSTEM 36 2.13
RADIAN SYSTEM 37 CHAPTER 3 TRIGONOMETRY 40 3.1 INTRODUCTION 40 3.2
FUNCTIONS OF ANGLES 40 3.3 THE COSINE AND SECANT FUNCTION 41 3.4 THE
COSINE FORMULA FOR A PLANE TRIANGLE 43 3.5 ANGLES GREATER THAN A RIGHT
ANGLE 45 3.6 COORDINATE AXES AND BEARINGS 48 3.7 DIRECTION COSINES ^ 50
3.8 OTHER TRIGONOMETRICAL FUNCTIONS 50 3.9 THE SINE RULE IN TRIANGLE ABC
51 3.10 THE TANGENT OF THE ANGLE 0 OR TAN 6 54 3.11 THE INVERSE
FUNCTIONS SIN 1 AND TAN 1 54 3.12 COSECANT AND COTANGENT 54 3.13
SUMMARY OF THE TRIGONOMETRICAL FUNCTIONS 55 3.14 THE COSINE AND SINE OF
THE COMPOUND ANGLE (A + B) 55 3.15 EXPRESSION FOR COS (A + B) 57 3.16
EXPRESSIONS FOR SIN (A - JB) AND COS (A - B) 58 3.17 EXPRESSION FOR TAN
(A + B) 58 3.18 EXPRESSIONS FOR SIN 2A AND COS 2A 58 3.19 EXPRESSIONS
FOR SIN 3A AND COS 3A 59 3.20 EXPRESSIONS FOR SUMS AND DIFFERENCES IN
TERMS OF HALF ANGLES 59 3.21 HALF ANGLE FORMULAE 60 3.22 HERO S FORMULA
FOR THE AREA OF A TRIANGLE 61 CHAPTER 4 PLANE COORDINATES 63 4.1 PLANE
COORDINATES IN MAP MAKING 63 4.2 CARTESIAN COORDINATES (X, Y) 64 4.3
PLANE POLAR COORDINATES (R, U) 65 4.4 CONVERSION OF POLAR AND CARTESIAN
COORDINATES 66 4.5 COORDINATE DIFFERENCES 67 4.6 MATHEMATICAL
EXPRESSIONS FOR A STRAIGHT LINE 68 4.7 POLAR EQUATION OF A LINE IN A
PLANE 71 4.8 PARAMETRIC EQUATIONS OF A LINE IN A PLANE 72 4.9 ANGLE
BETWEEN TWO LINES 75 CONTENTS /VII 4.10 THE EQUATION OF A CIRCLE 76 4.11
TANGENT TO A CIRCLE 78 4.12 LENGTH OF A TANGENT TO A CIRCLE FROM A GIVEN
EXTERNAL POINT 78 4.13 EQUATION OF A TANGENT TO A POINT ON A CIRCLE 79
4.14 FITTING A CIRCLE TO THREE TANGENTS 80 CHAPTER 5 PROBLEMS IN THREE
DIMENSIONS 83 5.1 REFERENCE SYSTEMS 83 5.2 A THREE-DIMENSIONAL MODEL 85
5.3 SIGNS AND COORDINATE DIFFERENCES 87 5.4 DIRECTED STEPS 88 5.5 LENGTH
OF A LINE 89 5.6 POLAR TO RECTANGULAR COORDINATES IN THREE DIMENSIONS 90
5.7 COORDINATE DIFFERENCES 91 5.8 DIRECTION COSINES IN THREE DIMENSIONS
92 5.9 EQUATIONS OF A LINE IN THREE DIMENSIONS 94 5.10 THE ANGLE BETWEEN
TWO RAYS 97 5.11 PARALLEL AND PERPENDICULAR RAYS 99 5.12 PROJECTION OF
ONE RAY ON ANOTHER ^ 100 5.13 DISTANCE FROM A POINT TO A RAY 101 5.14
THE COMMON NORMAL TO TWO RAYS 102 5.15 THE LENGTH OF THE NORMAL EF 103
5.16 TERMINALS OF THE COMMON NORMAL EF 103 5.17 THE EQUATION OF A PLANE
104 5.18 THE EQUATION OF A SPHERE 106 5.19 THE EQUATION OF A SPHERE FROM
FOUR KNOWN POINTS 106 5.20 FITTING TO A CIRCLE IN THREE DIMENSIONS 107
5.21 CREATION OF A STEREOSCOPIC IMAGE 109 CHAPTER 6 AREAS AND VOLUMES
115 6.1 AREAS OF PLANE FIGURES 115 6.2 AREA OF A TRIANGLE 115 6.3 AREA
OF A TRAPEZIUM 116 6.4 AREA OF A TRIANGLE IN TERMS OF PLANE COORDINATES
116 6.5 EXTENSION TO POLYGON 118 6.6 DETERMINANTS 119 6.7 THE
TETRAHEDRON 122 6.8 VOLUME OF THE TETRAHEDRON 123 6.9 VOLUME OF THE
TETRAHEDRON FROM COORDINATES 124 CHAPTER 7 MATRICES 133 7.1 MATRICES 133
7.2 AN INTRODUCTION TO MATRIX ALGEBRA 133 7.3 SOLUTION BY ELIMINATION
134 7.4 MATRIX NOTATION 136 VIN/ MATHS FOR MAP MAKERS 7.5 MATRIX
MULTIPLICATION 137 7.6 THE INVERSE OF A MATRIX 139 7.7 THE INVERSE OF A
SQUARE MATRIX 142 7.8 INVERSE OF A (2 X 2) MATRIX BY CRAMER S RULE 143
7.9 SINGULAR MATRICES 144 7.10 MORE MATRIX MULTIPLICATION 144 7.11 OTHER
MATRIX OPERATIONS: ADDITION AND SUBTRACTION 146 7.12 THE TRANSPOSE OF A
MATRIX 147 7.13 FURTHER OPERATIONS ON MATRICES 147 7.14 OPERATIONS ON
MATRIX PRODUCTS: REVERSAL RULE 148 7.15 SOME APPLICATIONS OF MATRIX
ALGEBRA 149 7.16 ROTATIONS IN THREE DIMENSIONS 150 7.17 STRUCTURE OF THE
ROTATION MATRIX 152 7.18 ROTATION OF SOLID BODY ABOUT THE OY AND OZ AXES
153 7.19 REVERSE CASE OF ROTATION 155 7.20 ORTHOGONAL MATRICES 156 7.21
COORDINATE TRANSFORMATIONS IN THREE DIMENSIONS 158 7.22 THE REVERSE
TRANSFORMATIONS 161 CHAPTER 8 VECTOR S 164 8.1 VECTORS 164 8.2 VECTOR
ALGEBRA 164 8.3 TRIANGLE ABC 165 8.4 FREE VECTORS AND POSITION VECTORS
166 8.5 ORTHOGONAL UNIT VECTORS 166 8.6 COMPONENTS AND DIRECTION COSINES
167 8.7 LENGTH OF A VECTOR 167 8.8 MULTIPLICATION OF A VECTOR BY A
SCALAR 169 8.9 MULTIPLICATION OF VECTORS 169 8.10 SCALAR MULTIPLICATION
OR DOT PRODUCT 170 8.11 DOT PRODUCTS OF ORTHOGONAL UNIT VECTORS I, J,
AND K 170 8.12 DOT PRODUCT IN TERMS OF COMPONENTS 170 8.13 VECTOR
MULTIPLICATION OR CROSS PRODUCT 172 8.14 CROSS PRODUCTS OF ORTHOGONAL
UNIT VECTORS I, J, AND K 173 8.15 CROSS PRODUCT IN TERMS OF COMPONENTS
174 8.16 PARALLEL AND ORTHOGONAL VECTORS 175 8.17 THE SCALAR TRIPLE
PRODUCT 175 8.18 VOLUME IN TERMS OF POSITION VECTORS 177 8.19
COPLANARITY OF VECTORS 178 CHAPTER 9 CALCULUS 180 9.1 CALCULUS 180 9.2
FUNCTIONS 180 9.3 LIMITS OF FUNCTIONS 182 9.4 TANGENTS TO CURVES 183 9.5
GENERAL CASE 186 CONTENTS/IX 9.6 PROOF OF THE GENERAL RESULT 186 9.7
MULTIPLE PROBLEMS 187 9.8 SECOND AND HIGHER DIFFERENTIALS 188 9.9
MACLAURIN S THEOREM 188 9.10 DIFFERENTIATION OF TRIGONOMETRICAL
FUNCTIONS SIN X AND COS X 189 9.11 DERIVATIVE OF SIN X 191 9.12
DERIVATIVE OF COS* 191 9.13 THE DIFFERENTIALS OF E* AND IN X 193 9.14
TAYLOR S SERIES 195 9.15 DIFFERENTIATION OF A PRODUCT 197 9.16
DIFFERENTIATION OF A FUNCTION OF A FUNCTION 198 9.17 QUOTIENT RULE FOR
DIFFERENTIATION 200 9.18 PARTIAL DIFFERENTIATION 201 9.19 TOTAL
DIFFERENTIAL 202 9.20 LOGARITHMIC PARTIAL DIFFERENTIATION 204 9.21
CURVATURE 205 9.22 INTEGRAL CALCULUS 208 9.23 THE NOTATION FOR AN
INTEGRAL 210 9.24 GEOMETRICAL INTERPRETATION OF INTEGRATION 212 9.25
INTEGRATION LIMITS 212 9.26 AREAS BY INTEGRATION 213 9.27 SIMPSON S RULE
FOR APPROXIMATE INTEGRATION 214 9.28 PROPERTIES OF THE CIRCLE 215 9.29
PROPERTIES OF THE SPHERE F 216 9.30 THE NORMAL DISTRIBUTION FUNCTION 217
CHAPTER 10 CONIC SECTIONS 223 10.1 CONIC SECTIONS 223 10.2 SECTIONS OF A
CONE 223 10.3 CIRCLE 225 10.4 PARABOLA 230 10.5 ELLIPSE 231 10.6
EQUATION OF AN ELLIPSE 231 10.7 AREA OF AN ELLIPSE 233 10.8 SUM OF FOCAL
DISTANCES 234 10.9 FREEDOM EQUATIONS OF THE ELLIPSE 235 10.10 RADIUS OF
CURVATURE OF THE ELLIPSE 236 10.11 LENGTH OF THE NORMAL TO AN ELLIPSE
237 10.12 LENGTH OF AN ARC OF THE ELLIPSE 238 10.13 THE HYPERBOLA 239
10.14 RANGE DIFFERENCE PROPERTY 242 CHAPTER 11 SPHERICAL TRIGONOMETRY
245 11.1 INTRODUCTION 245 11.2 THE SPHERE 245 X/ MATHS FOR MAP MAKERS
11.3 11.4 11.5 11.6 11.7 11.8 11.9 11.10 11.11 11.12 11.13 11.14 11.15
11.16 11.17 11.18 TERL2 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9
12.10 12.11 12.12 12.13 12.14 12.15 12.16 12.17 THE SPHERICAL TRIANGLE
MODEL OF SPHERICAL TRIANGLE SPHERICAL TRIGONOMETRICAL FORMULAE PROOF OF
THE COSINE FORMULA PROOF OF THE SINE FORMULA PROOF OF THE COTANGENT
FORMULA SPHERICAL EXCESS NAVIGATION AND SPHERICAL TRIGONOMETRY DIRECTION
AT TAKE-OFF MAP PROJECTIONS OF A SPHERE OBLIQUE COORDINATE SYSTEM
STEREOGRAPHIC PROJECTION OF A SPHERE AZIMUTHAL PROPERTY OF THE
STEREOGRAPHIC PROJECTION CONFORMALITY OF THE STEREOGRAPHIC PROJECTION
SCALE FACTOR IN DIRECTION QF SCALE FACTOR IN DIRECTION ORTHOGONAL TO QF
SOLUTION OF EQUATIONS INTRODUCTION LINEAR EQUATIONS SIMULTANEOUS LINEAR
EQUATIONS CRAMER S RULE FOR THE SOLUTION OF LINEAR EQUATIONS DERIVATION
OF CRAMER S RULE FOR A (2 X 2) MATRIX NOTE ON CONSISTENCY OF LINEAR
EQUATIONS DIRECT SOLUTION BY LU DECOMPOSITION GAUSSIAN ELIMINATION
DECOMPOSITION FORWARD SOLUTION BACK SOLUTION INVERSE OF N THE SOLUTION
OF A QUADRATIC EQUATION GRAPHIC SOLUTION OF EQUATIONS SOLUTION OF A
CUBIC EQUATION NEWTON S METHOD OF SOLUTION OF NON-LINEAR EQUATIONS
FORMAL STATEMENT OF NEWTON S METHOD REFERENCES APPENDIX USEFUL DATA
SUMMARY OF FORMULAE INDEX 246 246 247 247 249 249 250 252 253 254 254
256 256 258 258 259 261 261 262 262 265 266 267 267 268 269 270 270 271
273 274 276 280 281 285 286 289 301
|
| any_adam_object | 1 |
| author | Allan, Arthur L. |
| author_GND | (DE-588)142349453 |
| author_facet | Allan, Arthur L. |
| author_role | aut |
| author_sort | Allan, Arthur L. |
| author_variant | a l a al ala |
| building | Verbundindex |
| bvnumber | BV012006044 |
| classification_rvk | RB 10103 |
| ctrlnum | (OCoLC)473723150 (DE-599)BVBBV012006044 |
| discipline | Geographie |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01256nam a2200337 c 4500</leader><controlfield tag="001">BV012006044</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">980616s1997 d||| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1870325915</subfield><subfield code="9">1-870325-91-5</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)473723150</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV012006044</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-703</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">RB 10103</subfield><subfield code="0">(DE-625)142220:12616</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Allan, Arthur L.</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)142349453</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Maths for map makers</subfield><subfield code="c">by Arthur Allan</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Latheronwheel</subfield><subfield code="b">Whittles</subfield><subfield code="c">1997</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XIII, 305 S.</subfield><subfield code="b">graph. Darst.</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Kartografie</subfield><subfield code="0">(DE-588)4029823-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Kartografie</subfield><subfield code="0">(DE-588)4029823-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematik</subfield><subfield code="0">(DE-588)4037944-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">GBV Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008124783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-008124783</subfield></datafield></record></collection> |
| id | DE-604.BV012006044 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:20:03Z |
| institution | BVB |
| isbn | 1870325915 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008124783 |
| oclc_num | 473723150 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | XIII, 305 S. graph. Darst. |
| publishDate | 1997 |
| publishDateSearch | 1997 |
| publishDateSort | 1997 |
| publisher | Whittles |
| record_format | marc |
| spelling | Allan, Arthur L. Verfasser (DE-588)142349453 aut Maths for map makers by Arthur Allan Latheronwheel Whittles 1997 XIII, 305 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Kartografie (DE-588)4029823-1 gnd rswk-swf Mathematik (DE-588)4037944-9 gnd rswk-swf Kartografie (DE-588)4029823-1 s Mathematik (DE-588)4037944-9 s DE-604 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008124783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Allan, Arthur L. Maths for map makers Kartografie (DE-588)4029823-1 gnd Mathematik (DE-588)4037944-9 gnd |
| subject_GND | (DE-588)4029823-1 (DE-588)4037944-9 |
| title | Maths for map makers |
| title_auth | Maths for map makers |
| title_exact_search | Maths for map makers |
| title_full | Maths for map makers by Arthur Allan |
| title_fullStr | Maths for map makers by Arthur Allan |
| title_full_unstemmed | Maths for map makers by Arthur Allan |
| title_short | Maths for map makers |
| title_sort | maths for map makers |
| topic | Kartografie (DE-588)4029823-1 gnd Mathematik (DE-588)4037944-9 gnd |
| topic_facet | Kartografie Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008124783&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT allanarthurl mathsformapmakers |