Home » Archimedes archive » Acorn User » AU 1997-01 B.adf » Regulars » StarInfo/Allen/!Ignotum/Formulae/Formulae/Geom
StarInfo/Allen/!Ignotum/Formulae/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 » Acorn User » AU 1997-01 B.adf » Regulars |
| Filename: | StarInfo/Allen/!Ignotum/Formulae/Formulae/Geom |
| Read OK: | ✔ |
| File size: | 07F2 bytes |
| Load address: | 0000 |
| Exec address: | 0000 |
File contents
# Maths > Geometry # New entries should take the form of: # Formula # Note 1 # Note 2 # Note 3 # Note 4 # Note 5 # Formula # Note 1 # And so on... # To fit snugly into the window, each line should be no longer # than 42 characters. # There is a limit of 25 formulas per topic. # Any notes should be made here, at the beginning and should # be preceeded by a hash (#). 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 0a 23 20 4e 65 77 20 65 6e 74 72 69 65 |ry..# New entrie| 00000020 73 20 73 68 6f 75 6c 64 20 74 61 6b 65 20 74 68 |s should take th| 00000030 65 20 66 6f 72 6d 20 6f 66 3a 0a 23 20 20 20 20 |e form of:.# | 00000040 20 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 4e | Formula.# N| 00000050 6f 74 65 20 31 0a 23 20 20 20 20 20 4e 6f 74 65 |ote 1.# Note| 00000060 20 32 0a 23 20 20 20 20 20 4e 6f 74 65 20 33 0a | 2.# Note 3.| 00000070 23 20 20 20 20 20 4e 6f 74 65 20 34 0a 23 20 20 |# Note 4.# | 00000080 20 20 20 4e 6f 74 65 20 35 0a 23 20 20 20 20 20 | Note 5.# | 00000090 46 6f 72 6d 75 6c 61 0a 23 20 20 20 20 20 4e 6f |Formula.# No| 000000a0 74 65 20 31 0a 23 20 20 20 20 20 41 6e 64 20 73 |te 1.# And s| 000000b0 6f 20 6f 6e 2e 2e 2e 0a 23 20 54 6f 20 66 69 74 |o on....# To fit| 000000c0 20 73 6e 75 67 6c 79 20 69 6e 74 6f 20 74 68 65 | snugly into the| 000000d0 20 77 69 6e 64 6f 77 2c 20 65 61 63 68 20 6c 69 | window, each li| 000000e0 6e 65 20 73 68 6f 75 6c 64 20 62 65 20 6e 6f 20 |ne should be no | 000000f0 6c 6f 6e 67 65 72 0a 23 20 74 68 61 6e 20 34 32 |longer.# than 42| 00000100 20 63 68 61 72 61 63 74 65 72 73 2e 0a 23 20 54 | characters..# T| 00000110 68 65 72 65 20 69 73 20 61 20 6c 69 6d 69 74 20 |here is a limit | 00000120 6f 66 20 32 35 20 66 6f 72 6d 75 6c 61 73 20 70 |of 25 formulas p| 00000130 65 72 20 74 6f 70 69 63 2e 0a 0a 23 20 41 6e 79 |er topic...# Any| 00000140 20 6e 6f 74 65 73 20 73 68 6f 75 6c 64 20 62 65 | notes should be| 00000150 20 6d 61 64 65 20 68 65 72 65 2c 20 61 74 20 74 | made here, at t| 00000160 68 65 20 62 65 67 69 6e 6e 69 6e 67 20 61 6e 64 |he beginning and| 00000170 20 73 68 6f 75 6c 64 0a 23 20 62 65 20 70 72 65 | should.# be pre| 00000180 63 65 65 64 65 64 20 62 79 20 61 20 68 61 73 68 |ceeded by a hash| 00000190 20 28 23 29 2e 0a 0a 79 3d 6d 78 2b 63 0a 47 65 | (#)...y=mx+c.Ge| 000001a0 6e 65 72 61 6c 20 65 71 75 61 74 69 6f 6e 20 66 |neral equation f| 000001b0 6f 72 20 61 20 73 74 72 61 69 67 68 74 20 6c 69 |or a straight li| 000001c0 6e 65 2e 0a 6d 3d 67 72 61 64 69 65 6e 74 20 6f |ne..m=gradient o| 000001d0 66 20 6c 69 6e 65 0a 63 3d 69 6e 74 65 72 63 65 |f line.c=interce| 000001e0 70 74 20 6f 6e 20 79 20 61 78 69 73 0a 0a 0a 79 |pt on y axis...y| 000001f0 2d 79 31 3d 6d 28 78 2d 78 31 29 0a 55 73 65 64 |-y1=m(x-x1).Used| 00000200 20 74 6f 20 67 65 74 20 61 20 73 74 72 61 69 67 | to get a straig| 00000210 68 74 20 6c 69 6e 65 20 65 71 75 61 74 69 6f 6e |ht line equation| 00000220 20 77 68 65 6e 0a 79 6f 75 20 61 72 65 20 67 69 | when.you are gi| 00000230 76 65 6e 20 74 68 65 20 67 72 61 64 69 65 6e 74 |ven the gradient| 00000240 20 28 6d 29 20 61 6e 64 20 61 20 73 65 74 0a 6f | (m) and a set.o| 00000250 66 20 63 6f 2d 6f 72 64 69 6e 61 74 65 73 20 28 |f co-ordinates (| 00000260 78 31 2c 79 31 29 2e 0a 0a 0a 28 79 2d 79 31 29 |x1,y1)....(y-y1)| 00000270 2f 28 79 32 2d 79 31 29 3d 28 78 2d 78 31 29 2f |/(y2-y1)=(x-x1)/| 00000280 28 78 32 2d 78 31 29 0a 55 73 65 64 20 74 6f 20 |(x2-x1).Used to | 00000290 67 65 74 20 61 20 73 74 72 61 69 67 68 74 20 6c |get a straight l| 000002a0 69 6e 65 20 65 71 75 61 74 69 6f 6e 20 77 68 65 |ine equation whe| 000002b0 6e 0a 79 6f 75 20 61 72 65 20 67 69 76 65 6e 20 |n.you are given | 000002c0 74 77 6f 20 73 65 74 73 20 6f 66 20 63 6f 2d 6f |two sets of co-o| 000002d0 72 64 69 6e 61 74 65 73 2c 0a 28 78 31 2c 79 31 |rdinates,.(x1,y1| 000002e0 29 20 61 6e 64 20 28 78 31 2c 79 32 29 2e 0a 0a |) and (x1,y2)...| 000002f0 0a 6d 31 20 d7 20 6d 32 3d 2d 31 0a 46 6f 72 20 |.m1 . m2=-1.For | 00000300 73 74 72 61 69 67 68 74 20 6c 69 6e 65 73 20 70 |straight lines p| 00000310 65 72 70 65 6e 64 69 63 75 6c 61 72 20 74 6f 20 |erpendicular to | 00000320 65 61 63 68 0a 6f 74 68 65 72 3a 0a 54 68 65 20 |each.other:.The | 00000330 74 77 6f 20 67 72 61 64 69 65 6e 74 73 20 28 6d |two gradients (m| 00000340 31 20 61 6e 64 20 6d 32 29 20 6d 75 6c 74 69 70 |1 and m2) multip| 00000350 6c 69 65 64 0a 74 6f 67 65 74 68 65 72 20 65 71 |lied.together eq| 00000360 75 61 6c 73 20 2d 31 2e 0a 0a 74 61 6e 41 3d 7c |uals -1...tanA=|| 00000370 28 6d 31 2d 6d 32 29 2f 28 31 2b 6d 31 6d 32 29 |(m1-m2)/(1+m1m2)| 00000380 7c 0a 57 68 65 72 65 20 41 20 69 73 20 74 68 65 ||.Where A is the| 00000390 20 61 63 75 74 65 20 61 6e 67 6c 65 20 62 65 74 | acute angle bet| 000003a0 77 65 65 6e 20 74 77 6f 0a 73 74 72 61 69 67 68 |ween two.straigh| 000003b0 74 20 6c 69 6e 65 73 20 77 69 74 68 20 67 72 61 |t lines with gra| 000003c0 64 69 65 6e 74 73 20 6d 31 20 61 6e 64 20 6d 32 |dients m1 and m2| 000003d0 2e 0a 0a 0a 0a 6c 69 6e 65 20 6c 65 6e 67 74 68 |.....line length| 000003e0 3d 28 78 b2 2b 79 b2 2b 7a b2 29 5e bd 0a 54 68 |=(x.+y.+z.)^..Th| 000003f0 65 20 6c 65 6e 67 74 68 20 6f 66 20 61 20 6c 69 |e length of a li| 00000400 6e 65 20 65 71 75 61 6c 73 20 74 68 65 20 73 71 |ne equals the sq| 00000410 75 61 72 65 0a 72 6f 6f 74 20 6f 66 20 69 74 73 |uare.root of its| 00000420 20 78 2c 20 79 20 28 61 6e 64 20 70 6f 73 73 69 | x, y (and possi| 00000430 62 6c 79 20 7a 29 0a 63 6f 6d 70 6f 6e 65 6e 74 |bly z).component| 00000440 73 20 73 71 75 61 72 65 64 20 61 6e 64 20 61 64 |s squared and ad| 00000450 64 65 64 20 74 6f 67 65 74 68 65 72 2e 0a 28 46 |ded together..(F| 00000460 72 6f 6d 20 70 79 74 68 61 67 6f 72 61 73 27 73 |rom pythagoras's| 00000470 20 74 68 65 6f 72 65 6d 29 2e 0a 0a 78 3d 61 2b | theorem)...x=a+| 00000480 72 63 6f 73 74 20 61 6e 64 20 79 3d 62 2b 72 73 |rcost and y=b+rs| 00000490 69 6e 74 0a 50 61 72 61 6d 65 74 72 69 63 20 65 |int.Parametric e| 000004a0 71 75 61 74 69 6f 6e 73 20 66 6f 72 20 70 6c 6f |quations for plo| 000004b0 74 74 69 6e 67 20 61 0a 63 69 72 63 6c 65 2e 0a |tting a.circle..| 000004c0 43 65 6e 74 72 65 20 6f 66 20 63 69 72 63 6c 65 |Centre of circle| 000004d0 20 69 73 20 61 74 20 28 61 2c 62 29 0a 72 3d 72 | is at (a,b).r=r| 000004e0 61 64 69 75 73 0a 74 3d 61 6e 79 20 6e 75 6d 62 |adius.t=any numb| 000004f0 65 72 0a 28 78 2d 61 29 b2 2b 28 79 2d 62 29 b2 |er.(x-a).+(y-b).| 00000500 3d 72 b2 0a 43 61 72 74 65 73 69 61 6e 20 65 71 |=r..Cartesian eq| 00000510 75 61 74 69 6f 6e 20 66 6f 72 20 70 6c 6f 74 74 |uation for plott| 00000520 69 6e 67 20 61 20 63 69 72 63 6c 65 2e 0a 43 65 |ing a circle..Ce| 00000530 6e 74 72 65 20 6f 66 20 63 69 72 63 6c 65 20 69 |ntre of circle i| 00000540 73 20 61 74 20 28 61 2c 62 29 0a 72 3d 72 61 64 |s at (a,b).r=rad| 00000550 69 75 73 0a 0a 0a 41 3d 50 49 72 b2 0a 57 68 65 |ius...A=PIr..Whe| 00000560 72 65 3a 0a 41 3d 61 72 65 61 20 6f 66 20 61 20 |re:.A=area of a | 00000570 63 69 72 63 6c 65 0a 50 49 3d 33 2e 31 34 31 35 |circle.PI=3.1415| 00000580 39 32 36 34 35 0a 72 3d 72 61 64 69 75 73 20 6f |92645.r=radius o| 00000590 66 20 63 69 72 63 6c 65 0a 0a 63 3d 32 50 49 72 |f circle..c=2PIr| 000005a0 0a 57 68 65 72 65 3a 0a 63 3d 63 69 72 63 75 6d |.Where:.c=circum| 000005b0 66 65 72 65 6e 63 65 20 6f 66 20 61 20 63 69 72 |ference of a cir| 000005c0 63 6c 65 0a 50 49 3d 33 2e 31 34 31 35 39 32 36 |cle.PI=3.1415926| 000005d0 34 35 0a 72 3d 72 61 64 69 75 73 0a 0a 73 3d 72 |45.r=radius..s=r| 000005e0 41 0a 57 68 65 72 65 3a 0a 73 3d 73 65 63 74 69 |A.Where:.s=secti| 000005f0 6f 6e 20 6f 66 20 61 20 63 69 72 63 6c 65 27 73 |on of a circle's| 00000600 20 63 69 72 63 75 6d 66 65 72 65 6e 63 65 0a 72 | circumference.r| 00000610 3d 72 61 64 69 75 73 0a 41 20 69 73 20 61 6e 20 |=radius.A is an | 00000620 61 6e 67 6c 65 20 69 6e 20 72 61 64 69 61 6e 73 |angle in radians| 00000630 0a 4e 6f 74 65 3a 20 50 49 20 72 61 64 69 61 6e |.Note: PI radian| 00000640 73 3d 31 38 30 b0 0a 41 3d bd 72 b2 42 0a 57 68 |s=180..A=.r.B.Wh| 00000650 65 72 65 3a 0a 41 3d 61 72 65 61 20 6f 66 20 61 |ere:.A=area of a| 00000660 20 63 69 72 63 6c 65 20 73 65 67 6d 65 6e 74 0a | circle segment.| 00000670 72 3d 72 61 64 69 75 73 0a 42 20 69 73 20 61 6e |r=radius.B is an| 00000680 20 61 6e 67 6c 65 20 69 6e 20 72 61 64 69 61 6e | angle in radian| 00000690 73 0a 4e 6f 74 65 3a 20 50 49 20 72 61 64 69 61 |s.Note: PI radia| 000006a0 6e 73 3d 31 38 30 b0 0a 41 3d bd 61 62 73 69 6e |ns=180..A=.absin| 000006b0 43 0a 57 68 65 72 65 3a 0a 41 3d 61 72 65 61 20 |C.Where:.A=area | 000006c0 6f 66 20 61 20 74 72 69 61 6e 67 6c 65 0a 61 20 |of a triangle.a | 000006d0 61 6e 64 20 62 20 61 72 65 20 73 69 64 65 20 6c |and b are side l| 000006e0 65 6e 67 74 68 73 0a 43 3d 61 6e 67 6c 65 20 62 |engths.C=angle b| 000006f0 65 74 77 65 65 6e 20 61 20 61 6e 64 20 62 0a 4e |etween a and b.N| 00000700 6f 74 65 3a 20 49 74 20 77 6f 72 6b 73 20 6f 6e |ote: It works on| 00000710 20 61 6e 79 20 74 72 69 61 6e 67 6c 65 0a 41 3d | any triangle.A=| 00000720 28 73 28 73 2d 61 29 28 73 2d 62 29 28 73 2d 63 |(s(s-a)(s-b)(s-c| 00000730 29 29 5e bd 0a 4b 6e 6f 77 6e 20 61 73 20 48 65 |))^..Known as He| 00000740 72 6f 27 73 20 66 6f 72 6d 75 6c 61 2c 20 77 68 |ro's formula, wh| 00000750 65 72 65 3a 0a 41 3d 61 72 65 61 20 6f 66 20 61 |ere:.A=area of a| 00000760 20 74 72 69 61 6e 67 6c 65 0a 61 2c 20 62 20 61 | triangle.a, b a| 00000770 6e 64 20 63 20 61 72 65 20 73 69 64 65 20 6c 65 |nd c are side le| 00000780 6e 67 74 68 73 0a 73 3d bd 28 61 2b 62 2b 63 29 |ngths.s=.(a+b+c)| 00000790 0a 4e 6f 74 65 3a 20 49 74 20 77 6f 72 6b 73 20 |.Note: It works | 000007a0 6f 6e 20 61 6e 79 20 74 72 69 61 6e 67 6c 65 0a |on any triangle.| 000007b0 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a 0a |................| * 000007f0 0a 0a |..| 000007f2
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