[OT] pythageoron and 3d

[narf poit chez BOOM]

does anyone know the 3d equivalent to the pythageoron calculation?

[ April 30, 2003, 03:39: Message edited by: narf poit chez BOOM ]

[PvK]

Yes, just add a term for the third dimension.

I'm not sure what form you're looking for, but essentially:

d^2 = x^2 + y^2 + z^2

Where d is the distance you are probably looking for, and x, y, and z are the three right-angle coordinate displacements.

PvK

[Gwaihir]

just keep adding sides squared under the sqrt.

because the first diagonal is used as a side with the next "rectangular" side, so it looks like this (where a, b, c are the height, length, width, and you want the diagonal of the box):

diagonal of a side:
sqrt( a^2 + b^2 )

diagonal of box = diagonal of (diagonal of side & height):
sqrt( sqrt( a^2 + b^2 )^2 + c^2 )
=sqrt( a^2 + b^2 + c^2 )

so in an n-dimensional space, the distance from point p to point q is

sqrt( (p.1-q.1)^2 + (p.3-q.3)^2 + (p.3-q.3)^2 + . . . + (p.n-q.n)^2 )

(grr, how do you get &#nbsp; spaces to work? I can't do sigma notation without spaces to align the sub and superscritps. hrmph.)

hope that helps

edit: hehe, looks like i was beaten to it while i posted.

[ April 30, 2003, 00:38: Message edited by: Gwaihir ]

[Jack Simth]

Originally posted by Gwaihir:
just keep adding sides squared under the sqrt.

because the first diagonal is used as a side with the next "rectangular" side, so it looks like this (where a, b, c are the height, length, width, and you want the diagonal of the box):

diagonal of a side:
sqrt( a^2 + b^2 )

diagonal of box = diagonal of (diagonal of side & height):
sqrt( sqrt( a^2 + b^2 )^2 + c^2 )
=sqrt( a^2 + b^2 + c^2 )

so in an n-dimensional space, the distance from point p to point q is

sqrt( (p.1-q.1)^2 + (p.3-q.3)^2 + (p.3-q.3)^2 + . . . + (p.n-q.n)^2 )

(grr, how do you get &#nbsp; spaces to work? I can't do sigma notation without spaces to align the sub and superscritps. hrmph.)

&#num; where num is the number of the symbol you are looking for:
1 to 255 (but it goes higher):
1:&#1 2:&#2 3:&#3 4:&#4 5:&#5 6:&#6 7:&#7 8:&#8 9:&#9 10:&#10 11:&#11 12:&#12 13:&#13 14:&#14 15:&#15 16:&#16 17:&#17 18:&#18 19:&#19 20:&#20 21:&#21 22:&#22 23:&#23 24:&#24 25:&#25 26:&#26 27:&#27 28:&#28 29:&#29 30:&#30 31:&#31 32:&#32 33:&#33 34:&#34 35:&#35 36:&#36 37:&#37 38:&#38 39:&#39 40:&#40 41:&#41 42:&#42 43:&#43 44:&#44 45:&#45 46:&#46 47:&#47 48:&#48 49:&#49 50:&#50 51:&#51 52:&#52 53:&#53 54:&#54 55:&#55 56:&#56 57:&#57 58:&#58 59:&#59 60:&#60 61:&#61 62:&#62 63:&#63 64:&#64 65:&#65 66:&#66 67:&#67 68:&#68 69:&#69 70:&#70 71:&#71 72:&#72 73:&#73 74:&#74 75:&#75 76:&#76 77:&#77 78:&#78 79:&#79 80:&#80 81:&#81 82:&#82 83:&#83 84:&#84 85:&#85 86:&#86 87:&#87 88:&#88 89:&#89 90:&#90 91:&#91 92:&#92 93:&#93 94:&#94 95:&#95 96:&#96 97:&#97 98:&#98 99:&#99 100:&#100 101:&#101 102:&#102 103:&#103 104:&#104 105:&#105 106:&#106 107:&#107 108:&#108 109:&#109 110:&#110 111:&#111 112:&#112 113:&#113 114:&#114 115:&#115 116:&#116 117:&#117 118:&#118 119:&#119 120:&#120 121:&#121 122:&#122 123:&#123 124:&#124 125:&#125 126:&#126 127:&#127 128:&#128 129:&#129 130:&#130 131:&#131 132:&#132 133:&#133 134:&#134 135:&#135 136:&#136 137:&#137 138:&#138 139:&#139 140:&#140 141:&#141 142:&#142 143:&#143 144:&#144 145:&#145 146:&#146 147:&#147 148:&#148 149:&#149 150:&#150 151:&#151 152:&#152 153:&#153 154:&#154 155:&#155 156:&#156 157:&#157 158:&#158 159:&#159 160:&#160 161:&#161 162:&#162 163:&#163 164:&#164 165:&#165 166:&#166 167:&#167 168:&#168 169:&#169 170:&#170 171:&#171 172:&#172 173:&#173 174:&#174 175:&#175 176:&#176 177:&#177 178:&#178 179:&#179 180:&#180 181:&#181 182:&#182 183:&#183 184:&#184 185:&#185 186:&#186 187:&#187 188:&#188 189:&#189 190:&#190 191:&#191 192:&#192 193:&#193 194:&#194 195:&#195 196:&#196 197:&#197 198:&#198 199:&#199 200:&#200 201:&#201 202:&#202 203:&#203 204:&#204 205:&#205 206:&#206 207:&#207 208:&#208 209:&#209 210:&#210 211:&#211 212:&#212 213:&#213 214:&#214 215:&#215 216:&#216 217:&#217 218:&#218 219:&#219 220:&#220 221:&#221 222:&#222 223:&#223 224:&#224 225:&#225 226:&#226 227:&#227 228:&#228 229:&#229 230:&#230 231:&#231 232:&#232 233:&#233 234:&#234 235:&#235 236:&#236 237:&#237 238:&#238 239:&#239 240:&#240 241:&#241 242:&#242 243:&#243 244:&#244 245:&#245 246:&#246 247:&#247 248:&#248 249:&#249 250:&#250 251:&#251 252:&#252 253:&#253 254:&#254 255:&#255

Many of these can also be done with the alt-num method:
1 to 255 (does not go higher):
1:☺ 2:☻ 3:♥ 4:♦ 5:♣ 6:♠ 7:• 8:◘ 9:○ 10:◙ 11:♂ 12:♀ 13:♪ 14:♫ 15:☼ 16:► 17:◄ 18:↕ 19:‼ 20:¶ 21:§ 22:▬ 23:↨ 24:↑ 25:↓ 26:→ 27:← 28:∟ 29:↔ 30:▲ 31:▼ 32: 33:! 34:" 35:# 36:$ 37:% 38:& 39:' 40 41 42:* 43:+ 44:, 45:- 46:. 47:/ 48:0 49:1 50:2 51:3 52:4 53:5 54:6 55:7 56:8 57:9 58:: 59:; 60:< 61:= 62:> 63:? 64:@ 65:A 66:B 67:C 68 69:E 70:F 71:G 72:H 73:I 74:J 75:K 76:L 77:M 78:N 79:O 80:P 81:Q 82:R 83:S 84:T 85:U 86:V 87:W 88:X 89:Y 90:Z 91:[ 92:\ 93:]94:^ 95:_ 96:` 97:a 98:b 99:c 100:d 101:e 102:f 103:g 104:h 105:i 106:j 107:k 108:l 109:m 110:n 111 112 113:q 114:r 115:s 116:t 117:u 118:v 119:w 120:x 121:y 122:z 123:{ 124:| 125:} 126:~ 127:⌂ 128:Ç 129:ü 130:é 131:â 132:ä 133:à 134:å 135:ç 136:ê 137:ë 138:è 139:ï 140:î 141:ì 142:Ä 143:Å 144:É 145:æ 146:Æ 147:ô 148:ö 149:ò 150:û 151:ù 152:ÿ 153:Ö 154:Ü 155:¢ 156:£ 157:¥ 158:₧ 159:ƒ 160:á 161:í 162:ó 163:ú 164:ñ 165:Ñ 166:ª 167:º 168:¿ 169:⌐ 170:¬ 171:½ 172:¼ 173:¡ 174:« 175:» 176:░ 177:▒ 178:▓ 179:│ 180:┤ 181:╡ 182:╢ 183:╖ 184:╕ 185:╣ 186:║ 187:╗ 188:╝ 189:╜ 190:╛ 191:┐ 192:└ 193:┴ 194:┬ 195:├ 196:─ 197:┼ 198:╞ 199:╟ 200:╚ 201:╔ 202:╩ 203:╦ 204:╠ 205:═ 206:╬ 207:╧ 208:╨ 209:╤ 210:╥ 211:╙ 212:╘ 213:╒ 214:╓ 215:╫ 216:╪ 217:┘ 218:┌ 219:█ 220:▄ 221:▌ 222:▐ 223:▀ 224:α 225:ß 226:Γ 227:π 228:Σ 229:σ 230:µ 231:τ 232:Φ 233:Θ 234:Ω 235:δ 236:∞ 237:φ 238:ε 239:∩ 240:≡ 241:± 242:≥ 243:≤ 244:⌠ 245:⌡ 246:÷ 247:≈ 248:° 249:∙ 250:· 251:√ 252:ⁿ 253:² 254:■ 255: 
Note that the two tables are identicle between numbers 32 and 126.
Also, the Alt-method is implementation dependant over 126; you can't be sure how the other people will see it.
Also, it's a different table if you use a leading 0 (but I don't feel like posting it).

Originally posted by Gwaihir:

hope that helps

edit: hehe, looks like i was beaten to it while i posted.

Yes; but you posted the proof.

[ April 30, 2003, 01:45: Message edited by: Jack Simth ]

[Kamog]

Originally posted by Gwaihir:
(grr, how do you get &#nbsp; spaces to work? I can't do sigma notation without spaces to align the sub and superscritps. hrmph.)

You can have spaces by enclosing your text inside [ CODE ] [/ CODE ]

Like so:

code:

---

      n

sqrt( Σ ( p  -  q  )^2)

          i=1   i     i

---

But my sigma Σ turns into a different character, even though it looks correct when I typed it.
ALT-228 doesn't produce a sigma for me. I get this: _


Edit: now it changed into something else yet again, what's going on?

[ April 30, 2003, 01:48: Message edited by: Kamog ]

[Jack Simth]

Don't you just hate implementation dependance? Try finding one with the & # num; method.