Geometri - Links
Geometri - Links
Geometri - Links
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Indholdsfortegnelse<br />
Praktiske bemærkninger...................................................................................................................5<br />
Brug af bogen............................................................................................................................7<br />
Instruktion om opgaver på hjemmesider.............................................................................8<br />
Arven fra Grækenland......................................................................................................................9<br />
Græsk matematik...................................................................................................................11<br />
Ideernes verden.............................................................................................................12<br />
Sprogbrug......................................................................................................................12<br />
Hvad betyder det?........................................................................................................13<br />
Om at være nysgerrig og at se mønstre..............................................................................20<br />
Konstruktioner........................................................................................................................21<br />
At dele et linjestykke....................................................................................................22<br />
Ensvinklet - ligedannet..........................................................................................................26<br />
Ensvinklede trekanter..................................................................................................26<br />
Ligedannede trekanter.................................................................................................26<br />
Ligedannede og ensvinklede trekanter.....................................................................26<br />
Eksempel på beregninger............................................................................................28<br />
Model for skriftlige besvarelser..................................................................................29<br />
Euklid.......................................................................................................................................32<br />
Aksiomerne....................................................................................................................33<br />
Euklids første sætninger i bog 1.................................................................................34<br />
Kongruens......................................................................................................................34<br />
Kongruens (Definition)................................................................................................34<br />
Kongruens (Sætninger)................................................................................................35<br />
Nogle af Euklids øvrige sætninger fra bog I.............................................................35<br />
Astronomiske beregninger...................................................................................................37<br />
Jordens omkreds (Eratosthenes).................................................................................38<br />
Afstand til sol og måne I..............................................................................................39<br />
Afstand til sol og måne II (Aristarchos)....................................................................40<br />
Afstanden til månen.....................................................................................................41<br />
Trigonometri ....................................................................................................................................45<br />
Trekantsberegninger - en oversigt.......................................................................................47<br />
Korttegning.............................................................................................................................48<br />
Johannes Mejers kort....................................................................................................48<br />
Trianguleringen i Danmark.........................................................................................48<br />
Målebordsblade.............................................................................................................49<br />
Standardtrekanter..................................................................................................................51<br />
Definition: sin(A)..........................................................................................................53<br />
Definition: cos(A)..........................................................................................................53<br />
Sætning: mk = hyp*sin(v)............................................................................................54<br />
Sætning: hk = hyp*cos(v).............................................................................................54<br />
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