Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum » !Ignotum/Formulae/Geom
!Ignotum/Formulae/Geom
This website contains an archive of files for the Acorn Electron, BBC Micro, Acorn Archimedes, Commodore 16 and Commodore 64 computers, which Dominic Ford has rescued from his private collection of floppy disks and cassettes.
Some of these files were originally commercial releases in the 1980s and 1990s, but they are now widely available online. I assume that copyright over them is no longer being asserted. If you own the copyright and would like files to be removed, please contact me.
| Tape/disk: | Home » Archimedes archive » Archimedes World » AW-1996-07.adf » !Ignotum_Ignotum |
| Filename: | !Ignotum/Formulae/Geom |
| Read OK: | ✔ |
| File size: | 066E bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Geometry y=mx+c General equation for a straight line. m=gradient of line c=intercept on y axis y-y1=m(x-x1) Used to get a straight line equation when you are given the gradient (m) and a set of co-ordinates (x1,y1). (y-y1)/(y2-y1)=(x-x1)/(x2-x1) Used to get a straight line equation when you are given two sets of co-ordinates, (x1,y1) and (x1,y2). m1 � m2=-1 For straight lines perpendicular to each other: The two gradients (m1 and m2) multiplied together equals -1. tanA=|(m1-m2)/(1+m1m2)| Where A is the acute angle between two straight lines with gradients m1 and m2. line length=(x�+y�+z�)^� The length of a line equals the square root of its x, y (and possibly z) components squared and added together. (From pythagoras's theorem). x=a+rcost and y=b+rsint Parametric equations for plotting a circle. Centre of circle is at (a,b) r=radius t=any number (x-a)�+(y-b)�=r� Cartesian equation for plotting a circle. Centre of circle is at (a,b) r=radius A=PIr� Where: A=area of a circle PI=3.141592645 r=radius of circle c=2PIr Where: c=circumference of a circle PI=3.141592645 r=radius s=rA Where: s=section of a circle's circumference r=radius A is an angle in radians Note: PI radians=180� A=�r�B Where: A=area of a circle segment r=radius B is an angle in radians Note: PI radians=180� A=�absinC Where: A=area of a triangle a and b are side lengths C=angle between a and b Note: It works on any triangle A=(s(s-a)(s-b)(s-c))^� Known as Hero's formula, where: A=area of a triangle a, b and c are side lengths s=�(a+b+c) Note: It works on any triangle
00000000 23 20 4d 61 74 68 73 20 3e 20 47 65 6f 6d 65 74 |# Maths > Geomet| 00000010 72 79 0a 79 3d 6d 78 2b 63 0a 47 65 6e 65 72 61 |ry.y=mx+c.Genera| 00000020 6c 20 65 71 75 61 74 69 6f 6e 20 66 6f 72 20 61 |l equation for a| 00000030 20 73 74 72 61 69 67 68 74 20 6c 69 6e 65 2e 0a | straight line..| 00000040 6d 3d 67 72 61 64 69 65 6e 74 20 6f 66 20 6c 69 |m=gradient of li| 00000050 6e 65 0a 63 3d 69 6e 74 65 72 63 65 70 74 20 6f |ne.c=intercept o| 00000060 6e 20 79 20 61 78 69 73 0a 0a 0a 79 2d 79 31 3d |n y axis...y-y1=| 00000070 6d 28 78 2d 78 31 29 0a 55 73 65 64 20 74 6f 20 |m(x-x1).Used to | 00000080 67 65 74 20 61 20 73 74 72 61 69 67 68 74 20 6c |get a straight l| 00000090 69 6e 65 20 65 71 75 61 74 69 6f 6e 20 77 68 65 |ine equation whe| 000000a0 6e 0a 79 6f 75 20 61 72 65 20 67 69 76 65 6e 20 |n.you are given | 000000b0 74 68 65 20 67 72 61 64 69 65 6e 74 20 28 6d 29 |the gradient (m)| 000000c0 20 61 6e 64 20 61 20 73 65 74 0a 6f 66 20 63 6f | and a set.of co| 000000d0 2d 6f 72 64 69 6e 61 74 65 73 20 28 78 31 2c 79 |-ordinates (x1,y| 000000e0 31 29 2e 0a 0a 0a 28 79 2d 79 31 29 2f 28 79 32 |1)....(y-y1)/(y2| 000000f0 2d 79 31 29 3d 28 78 2d 78 31 29 2f 28 78 32 2d |-y1)=(x-x1)/(x2-| 00000100 78 31 29 0a 55 73 65 64 20 74 6f 20 67 65 74 20 |x1).Used to get | 00000110 61 20 73 74 72 61 69 67 68 74 20 6c 69 6e 65 20 |a straight line | 00000120 65 71 75 61 74 69 6f 6e 20 77 68 65 6e 0a 79 6f |equation when.yo| 00000130 75 20 61 72 65 20 67 69 76 65 6e 20 74 77 6f 20 |u are given two | 00000140 73 65 74 73 20 6f 66 20 63 6f 2d 6f 72 64 69 6e |sets of co-ordin| 00000150 61 74 65 73 2c 0a 28 78 31 2c 79 31 29 20 61 6e |ates,.(x1,y1) an| 00000160 64 20 28 78 31 2c 79 32 29 2e 0a 0a 0a 6d 31 20 |d (x1,y2)....m1 | 00000170 d7 20 6d 32 3d 2d 31 0a 46 6f 72 20 73 74 72 61 |. m2=-1.For stra| 00000180 69 67 68 74 20 6c 69 6e 65 73 20 70 65 72 70 65 |ight lines perpe| 00000190 6e 64 69 63 75 6c 61 72 20 74 6f 20 65 61 63 68 |ndicular to each| 000001a0 0a 6f 74 68 65 72 3a 0a 54 68 65 20 74 77 6f 20 |.other:.The two | 000001b0 67 72 61 64 69 65 6e 74 73 20 28 6d 31 20 61 6e |gradients (m1 an| 000001c0 64 20 6d 32 29 20 6d 75 6c 74 69 70 6c 69 65 64 |d m2) multiplied| 000001d0 0a 74 6f 67 65 74 68 65 72 20 65 71 75 61 6c 73 |.together equals| 000001e0 20 2d 31 2e 0a 0a 74 61 6e 41 3d 7c 28 6d 31 2d | -1...tanA=|(m1-| 000001f0 6d 32 29 2f 28 31 2b 6d 31 6d 32 29 7c 0a 57 68 |m2)/(1+m1m2)|.Wh| 00000200 65 72 65 20 41 20 69 73 20 74 68 65 20 61 63 75 |ere A is the acu| 00000210 74 65 20 61 6e 67 6c 65 20 62 65 74 77 65 65 6e |te angle between| 00000220 20 74 77 6f 0a 73 74 72 61 69 67 68 74 20 6c 69 | two.straight li| 00000230 6e 65 73 20 77 69 74 68 20 67 72 61 64 69 65 6e |nes with gradien| 00000240 74 73 20 6d 31 20 61 6e 64 20 6d 32 2e 0a 0a 0a |ts m1 and m2....| 00000250 0a 6c 69 6e 65 20 6c 65 6e 67 74 68 3d 28 78 b2 |.line length=(x.| 00000260 2b 79 b2 2b 7a b2 29 5e bd 0a 54 68 65 20 6c 65 |+y.+z.)^..The le| 00000270 6e 67 74 68 20 6f 66 20 61 20 6c 69 6e 65 20 65 |ngth of a line e| 00000280 71 75 61 6c 73 20 74 68 65 20 73 71 75 61 72 65 |quals the square| 00000290 0a 72 6f 6f 74 20 6f 66 20 69 74 73 20 78 2c 20 |.root of its x, | 000002a0 79 20 28 61 6e 64 20 70 6f 73 73 69 62 6c 79 20 |y (and possibly | 000002b0 7a 29 0a 63 6f 6d 70 6f 6e 65 6e 74 73 20 73 71 |z).components sq| 000002c0 75 61 72 65 64 20 61 6e 64 20 61 64 64 65 64 20 |uared and added | 000002d0 74 6f 67 65 74 68 65 72 2e 0a 28 46 72 6f 6d 20 |together..(From | 000002e0 70 79 74 68 61 67 6f 72 61 73 27 73 20 74 68 65 |pythagoras's the| 000002f0 6f 72 65 6d 29 2e 0a 0a 78 3d 61 2b 72 63 6f 73 |orem)...x=a+rcos| 00000300 74 20 61 6e 64 20 79 3d 62 2b 72 73 69 6e 74 0a |t and y=b+rsint.| 00000310 50 61 72 61 6d 65 74 72 69 63 20 65 71 75 61 74 |Parametric equat| 00000320 69 6f 6e 73 20 66 6f 72 20 70 6c 6f 74 74 69 6e |ions for plottin| 00000330 67 20 61 0a 63 69 72 63 6c 65 2e 0a 43 65 6e 74 |g a.circle..Cent| 00000340 72 65 20 6f 66 20 63 69 72 63 6c 65 20 69 73 20 |re of circle is | 00000350 61 74 20 28 61 2c 62 29 0a 72 3d 72 61 64 69 75 |at (a,b).r=radiu| 00000360 73 0a 74 3d 61 6e 79 20 6e 75 6d 62 65 72 0a 28 |s.t=any number.(| 00000370 78 2d 61 29 b2 2b 28 79 2d 62 29 b2 3d 72 b2 0a |x-a).+(y-b).=r..| 00000380 43 61 72 74 65 73 69 61 6e 20 65 71 75 61 74 69 |Cartesian equati| 00000390 6f 6e 20 66 6f 72 20 70 6c 6f 74 74 69 6e 67 20 |on for plotting | 000003a0 61 20 63 69 72 63 6c 65 2e 0a 43 65 6e 74 72 65 |a circle..Centre| 000003b0 20 6f 66 20 63 69 72 63 6c 65 20 69 73 20 61 74 | of circle is at| 000003c0 20 28 61 2c 62 29 0a 72 3d 72 61 64 69 75 73 0a | (a,b).r=radius.| 000003d0 0a 0a 41 3d 50 49 72 b2 0a 57 68 65 72 65 3a 0a |..A=PIr..Where:.| 000003e0 41 3d 61 72 65 61 20 6f 66 20 61 20 63 69 72 63 |A=area of a circ| 000003f0 6c 65 0a 50 49 3d 33 2e 31 34 31 35 39 32 36 34 |le.PI=3.14159264| 00000400 35 0a 72 3d 72 61 64 69 75 73 20 6f 66 20 63 69 |5.r=radius of ci| 00000410 72 63 6c 65 0a 0a 63 3d 32 50 49 72 0a 57 68 65 |rcle..c=2PIr.Whe| 00000420 72 65 3a 0a 63 3d 63 69 72 63 75 6d 66 65 72 65 |re:.c=circumfere| 00000430 6e 63 65 20 6f 66 20 61 20 63 69 72 63 6c 65 0a |nce of a circle.| 00000440 50 49 3d 33 2e 31 34 31 35 39 32 36 34 35 0a 72 |PI=3.141592645.r| 00000450 3d 72 61 64 69 75 73 0a 0a 73 3d 72 41 0a 57 68 |=radius..s=rA.Wh| 00000460 65 72 65 3a 0a 73 3d 73 65 63 74 69 6f 6e 20 6f |ere:.s=section o| 00000470 66 20 61 20 63 69 72 63 6c 65 27 73 20 63 69 72 |f a circle's cir| 00000480 63 75 6d 66 65 72 65 6e 63 65 0a 72 3d 72 61 64 |cumference.r=rad| 00000490 69 75 73 0a 41 20 69 73 20 61 6e 20 61 6e 67 6c |ius.A is an angl| 000004a0 65 20 69 6e 20 72 61 64 69 61 6e 73 0a 4e 6f 74 |e in radians.Not| 000004b0 65 3a 20 50 49 20 72 61 64 69 61 6e 73 3d 31 38 |e: PI radians=18| 000004c0 30 b0 0a 41 3d bd 72 b2 42 0a 57 68 65 72 65 3a |0..A=.r.B.Where:| 000004d0 0a 41 3d 61 72 65 61 20 6f 66 20 61 20 63 69 72 |.A=area of a cir| 000004e0 63 6c 65 20 73 65 67 6d 65 6e 74 0a 72 3d 72 61 |cle segment.r=ra| 000004f0 64 69 75 73 0a 42 20 69 73 20 61 6e 20 61 6e 67 |dius.B is an ang| 00000500 6c 65 20 69 6e 20 72 61 64 69 61 6e 73 0a 4e 6f |le in radians.No| 00000510 74 65 3a 20 50 49 20 72 61 64 69 61 6e 73 3d 31 |te: PI radians=1| 00000520 38 30 b0 0a 41 3d bd 61 62 73 69 6e 43 0a 57 68 |80..A=.absinC.Wh| 00000530 65 72 65 3a 0a 41 3d 61 72 65 61 20 6f 66 20 61 |ere:.A=area of a| 00000540 20 74 72 69 61 6e 67 6c 65 0a 61 20 61 6e 64 20 | triangle.a and | 00000550 62 20 61 72 65 20 73 69 64 65 20 6c 65 6e 67 74 |b are side lengt| 00000560 68 73 0a 43 3d 61 6e 67 6c 65 20 62 65 74 77 65 |hs.C=angle betwe| 00000570 65 6e 20 61 20 61 6e 64 20 62 0a 4e 6f 74 65 3a |en a and b.Note:| 00000580 20 49 74 20 77 6f 72 6b 73 20 6f 6e 20 61 6e 79 | It works on any| 00000590 20 74 72 69 61 6e 67 6c 65 0a 41 3d 28 73 28 73 | triangle.A=(s(s| 000005a0 2d 61 29 28 73 2d 62 29 28 73 2d 63 29 29 5e bd |-a)(s-b)(s-c))^.| 000005b0 0a 4b 6e 6f 77 6e 20 61 73 20 48 65 72 6f 27 73 |.Known as Hero's| 000005c0 20 66 6f 72 6d 75 6c 61 2c 20 77 68 65 72 65 3a | formula, where:| 000005d0 0a 41 3d 61 72 65 61 20 6f 66 20 61 20 74 72 69 |.A=area of a tri| 000005e0 61 6e 67 6c 65 0a 61 2c 20 62 20 61 6e 64 20 63 |angle.a, b and c| 000005f0 20 61 72 65 20 73 69 64 65 20 6c 65 6e 67 74 68 | are side length| 00000600 73 0a 73 3d bd 28 61 2b 62 2b 63 29 0a 4e 6f 74 |s.s=.(a+b+c).Not| 00000610 65 3a 20 49 74 20 77 6f 72 6b 73 20 6f 6e 20 61 |e: It works on a| 00000620 6e 79 20 74 72 69 61 6e 67 6c 65 0a 0a 0a 0a 0a |ny triangle.....| 00000630 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 00000660 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |..............| 0000066e
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