1. 1.
2. 2. W W K K ???? K K K
3. 3. FE K K W K
4. 4.
5. 5. -- W W K W W K K K K W K W W K W K K
6. 6. -- JFE KLinear measurements KAngular measurements W KHorizontal Distance measurementK KVertical Distance measurementK KSlope Distance measurementK W Angle MeasurementHorizontalK Vertical Angle MeasurementKFE
7. 7. -- Units of measurementK K W FWESI units (Metric system)K K KFE English systemK KFE FEUnits of length measurementsK FEW FMetreEFmE W 1000000 1 10 6 mMicrometreFE 1000 1 10 3 mmMillimetreFE 100 1 10 2 cmCentimetreFE 1000103 kmKilometreFE 1 mm = 1000 m 1 cm = 10 mm 1 m = 100 cm 1 km = 1000 m
8. 8. -- W F JEW1.97 mKmm W mm19701010097.1 F JEW55000 cmKkm W km55.01000100/55000 F J J JEW W ELLFinInchFE ELFftFootFE ydYardFE miMileFE 1 ft = 12 in 1 yd = 3 ft 1 mi = 1760 yd
9. 9. -- W FEWft300mi W 300/(31760)=0.0568 mi FEW K K K
10. 10. -- FWE 880 kmK W 8001000100/(2.541231760) =546.8066 mi FEW 100 ydK W 1003122.54/100=91.440 m FEunits of area measurementK W 100 mm2 =1010=Cm2 1 10000 cm2 =100100=m2 1 1000000 m2 =10001000=km2 1 10000 m2 =FEHectare(ha)1 1000 m2 =FEDonm1 FEW7813456 m2 W 7813456/1000000=7.813456 m2
11. 11. -- FEunits of volume measurementW W 1000 Liter=1000000 cm3 =m3 1 1000 cm3 =Liter1FE 4.546 Liter=Gallon1FE FEW36 m3 W 361000=36000 Liter FEW FEThe sexayesimal system 360(Degree) ( )( minute ) FEFsecondE FFEF JKEFE 1 circle = 360 1 = 60 1 = 60 W 78 45 34 W 45 21 27.49 F JE
12. 12. -- FEThe decimal or centesimal systemK 400FgradE FgE100 FCentesimal minuteEFc E100 FCentesimal secondE Fcc KEFE 1 circle=400 g =100 c 1g =100 cc 1c W 51.6731 g 51g 67 c 31cc W 400 gon=Circle1 centigon)(100 cgon=gon 1 milligon)(10 mgon=cgon1 K F JE
13. 13. -- J JRadian system Radian F JE Z2 rW Wr ( radius ) WF22/7EW 2857142866 7 44 7 22 222 .====r/r J JW W 2 = 3600 = 400 g RadianFGradianEDegree 2 400 g 360 180360 2 9 10 360 400 = 1 360 360 1 200400 2 1 400 400 = 90 10 9 400 360 .== 1 g l 2 2 200 2 400 180 2 360 1 rad F JE F JE
14. 14. -- FEW 64 18 20 W 64.30555556=)20/3600FHE18/60HE64 64.30555556 Z201864 FE K 64.30555556 9 10 =71.4506 g K Rad1.122344=F/180EC64.30555556 FEW 227.4589 g W W 204.713010=227.45890.9 204 42 46.84=FE F204E0.71301=204.71301 - 204 F42E42.7806 =0.7130160 FE46.84=600.7806
15. 15. -- W 3.572916 radFZ/200EC227.4589 FEW 2.137524 rad W W 122 28 16 =122.471104=F/180E2.137524 W 136.0790 g=F/200E2.137524
16. 16. -- 350 km 5000 m 1 ft 30 m 100 mi /hour 30 yd 10 km 2 2400 gallon 18 m3 45 385.4831 g 0.004218 rad 131 21 47 225.418 gon
17. 17. -- 1700 km 550 mi 180KA F JE F JE
18. 18.
19. 19. -- W W K W W K K K W K W W K W K
20. 20. -- F JEW W( n-dimensional )K WFE KFE GW K( Origin point )K K( Coordinates axes )K KK F JEW K K K J JCartesian Coordinates System Rectangular coordinates FxE FyE ( origin )F(0 , 0 )EK( x , y ) ( x )( y ) ( y )( x )K F JE
21. 21. -- F JKEFE F J JEPolar Coordinates System ( Pole ) ( Polar axis ) FE Fr , EW rWK W K Circular coordinates systemKFE F J JEW W F JEX = r cos F JEY = r sin F JE=22 Y+Xr F JE = x y tan1 F JE F JE FE
22. 22. -- FEFE W FKE Fx , y , zEx , y , z RKFx , y , zEWxy zKK Fx , y , zE FOrigin pointExx yy zzFKE FE FEWCylinderical coordinates : FEFr , , zEFr , EzFzE K Fr , , zE r zzK K W K KFE F JE F JE
23. 23. -- FEWWSherical coordinates system F , ,EW WFpointoriginKE WK W zK F , ,Ep z KFE FEWGeographical coordinates system K FE K K FEWLatitude ( ) K K180K F JE F JE
24. 24. -- FEWLongitude ( ) FE 360180180 K FEWK W F JErcosx = F JErsiny = F JEzz= F JE
25. 25. -- W F JE22 y+xr = F JE x y tan1 = F JEzz= FEWW W F JE 22 z+r = F JE = F JE z r tan1 = W FJE sin r = FJE= FJE cos z= F JE
26. 26. -- K F JE222 z+y+x = F JE x y tan1 = F JE z y+x tan 22 1 = K FJE sincosx = FJE sinsiny = FJEcosz=
27. 27.
28. 28. -- W W K W W K K W K W W K W K K
29. 29. -- F JEW K( Horizontal Distance ) KFEFE F JEW K( s )Slope Distance K( H )Horizontal DistanceK K( v )Vertical DistanceK Ftotal stationEK F JEW W
30. 30. -- F J JEW W F JEScos=H HWK SWK WKFE F JEW A , B249.510 m 2 22 41 WF JE Scos=H 249.510 cos (2 22 41 )= 249.295 m= F JE
31. 31. -- J JFE W F JE22 vsH W VWFEKFE F JEW124.567 mK 2.416 mK WF JE 22 VS=H ( ) ( )22 4162567124 ..= 124.544 m= F JE
32. 32. -- J J W F JEVcot= tan V =H F JE A , B 1.583 m00 58 43 WF JE Vcot=H tan v = 348500tan 583.1 = 92.673 m= F JE
33. 33. -- J JW K 1:1,1:2,2:3 T1 )( ( T2 )K ( G=2% )( G= 3% ) K100 m 2m3 m KFEFE W F JE2 2 2 12 t+t/st=H W H=K S=K t1=K t2=K F JE
34. 34. -- F JEW100 m 1 : 4K W 2 2 2 12 t+t/st=H 1611004 += 97.014 m= F JEW250 m G= 3%K W t2=100t1=3G=3% 2 2 2 12 t+t/st=H 100009250100 +/= 249.887 m= JW F J JE FE F JESsin=V VWFEFEFE FEW FKE W Ssin =V 249.51 SIN(02 22 41)= 10.353 m=
35. 35. -- FEWK FEFEW F JE22 HS=V FWE 124.567 mK 124.544 m W FE 22 HS =V ( ) ( )22 544124567124 ..= 2.394 m= WW FEFEW F JE tan cot H VVH tanHV FWE B , C74.584 m 01 20 34 W FE H tan=V 74.584 tan(01 20 34)= 1.748 m=
36. 36. -- FEWW FEFEW F JE2 2 2 11 t+t/st=V FWE FKE 2 2 2 11 t+t/st=V 22 41/1001 = 24.254 m= FFWE FE 2 2 2 11 t+t/st=V 23 10032503 +/= 7.497 m=
37. 37. -- Q1E 523.72 m1 49 55 Q2E S= 271.548 m V= 3.517 m H = ? Q3E5.451 m 5.418 gon Q4EFE Q5E174.521 m 173.953 m Q6EFE F JE
38. 38. -- ( Q7324.571 m 1 : 3 ( Q85% 524.34 m ( Q9Q8 , Q7 (Q10725.431 m25.432 yd
39. 39.
40. 40. -- W W K W W K K W K W K K W K K
41. 41. ---- F JEWW FE K FE K F JEW (X , Y )X , Y FNEKE EX NY FE,NEF J EK FrE FEFr , KE F JE E,N
42. 42. ---- F J JEW A A,BAB B F JEW F JEABABAB SINDE F JEABABAB COSDN F JEABAB EEE F JEABAB NNN W EAWAK NAWAK EBWBK NBWBK ABWABK DABWA,BK EABWA,BK NABWA,BK F JE