[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.

[Gwaihir]

So only some subset of HTML is actually allowed i guess.

I wrote a little javascript table maker to test ranges of #s for the $# method a while back, and I seem to recall that it goes up al least to the low 5-digits (there may be wrapping going on tho). Given the stuff i got in chunks at higher indices, i think that it may be different language add-ons or some such. Does anyone know if this is in fact the case?

Here's a pretty good listing, includes some chars up to 9830 (the diamond suit):
http://www.home.zonnet.nl/robschluter/htmltaglist/
(go to character set, near the bottom of the title bar's "page" list)

the alt-method actually inserts the character, so it won't work for space-making. It seems that only the Last 7 digits are used:
alt-789456123=√
alt-549456123=√
alt-9456123=√

AHA, it wraps at 65536:
alt-6 = ♠
alt-65542 = ♠
alt-500 = ⌠
alt-66036 = ⌠

Sadly, no really special characters like backspace and carriage return (the kind without the attached newline . . . *evil ☺*

interesting, i get a more complete set:
alt+
1:☺
2:☻
3:♥
4:♦
5:♣
6:♠
question, did smile, negative of smilie, heart, diamond, club, spade show on everyone else's system? I know the high chars are system-dependent, but i think the low chars may be as well.
edit: AHA! after posting, it went to the same as your list . . . and upon viewing the source, it appears that the special characters are not included in the HTML (of course this makes sense, it's stored in 1-byte plaintext) and therefore are converted to the appropriate ASCII &# code. However, the browser (i guess its the browser, although i thought that it handled those chars just fine before . . . guess i recall incorrectly) doensn't recognize some of them, so poof we get boxes.

Does anyone know what alt is calling on? is it a non-ASCII standard?

[ April 30, 2003, 02:40: Message edited by: Gwaihir ]

[narf poit chez BOOM]

thanks. turns out i was doing it right after all. i was worried i'd have to cube root it or something.

[ April 30, 2003, 03:37: Message edited by: narf poit chez BOOM ]

[Jack Simth]

Originally posted by Gwaihir:
So only some subset of HTML is actually allowed i guess.

I wrote a little javascript table maker to test ranges of #s for the $# method a while back, and I seem to recall that it goes up al least to the low 5-digits (there may be wrapping going on tho). Given the stuff i got in chunks at higher indices, i think that it may be different language add-ons or some such. Does anyone know if this is in fact the case?

I'm reasonably sure that is what is going on.

Originally posted by Gwaihir:

Here's a pretty good listing, includes some chars up to 9830 (the diamond suit):
http://www.home.zonnet.nl/robschluter/htmltaglist/
(go to character set, near the bottom of the title bar's "page" list)

the alt-method actually inserts the character, so it won't work for space-making. It seems that only the Last 7 digits are used:
alt-789456123=√
alt-549456123=√
alt-9456123=√

AHA, it wraps at 65536:
alt-6 = ♠
alt-65542 = ♠
alt-500 = ⌠
alt-66036 = ⌠

This one is done at a very basic level on your local computer; it wraps at 16 (65536) bits for you. On many computers, it wraps at 8 (256) bits.

Originally posted by Gwaihir:

Sadly, no really special characters like backspace and carriage return (the kind without the attached newline . . . *evil ☺*

interesting, i get a more complete set:
alt+
1:☺
2:☻
3:♥
4:♦
5:♣
6:♠
question, did smile, negative of smilie, heart, diamond, club, spade show on everyone else's system? I know the high chars are system-dependent, but i think the low chars may be as well.
edit: AHA! after posting, it went to the same as your list . . . and upon viewing the source, it appears that the special characters are not included in the HTML (of course this makes sense, it's stored in 1-byte plaintext) and therefore are converted to the appropriate ASCII &# code. However, the browser (i guess its the browser, although i thought that it handled those chars just fine before . . . guess i recall incorrectly) doensn't recognize some of them, so poof we get boxes.

The text box you enter stuff in and the way it is viewed are two different implementations, and have different abilities. This is why the difference. However, for amusement, I would suggest looking at it in different browsers, and from different computers, and in different OS's, so that you can see the varying differences.

Originally posted by Gwaihir:

Does anyone know what alt is calling on? is it a non-ASCII standard?

The Alt method runs at your machine before the data is sent to the forum; the &#num; method runs on the browser, after the data has come back. ASCII standard really only applies for 0-127; however, there isn't anything that requires a program use ASCII. It is just strongly advised for the majority of the set.

[Gwaihir]

It may be that it wraps earlier for me too, i was just too lazy to check.

Lessee:
alt-100:d
alt-356:d

hehe, there I go again with stupid assumptions (and we all know what assumptions do . . . ) I shoulda figured that it would wrap there when I saw that it used the 8000s and 9000s for #s in the 1-256 range. oops.

I wonder where the &# wraps though. I think its probably 65536, since its clearly not 256. Unless it does something weird and uses only part of a byte --- riiiiiiight.

I was just wondering if the ALT- method actually does comply with some standard, because there are a few smaller/older standards out there . . . a lot of the chars it produces are old DOS "graphic" characters, tree lines, borders, etc. (Yay DOS! wheeeee!) There must have been a standard for that.

I think I'll see if Linux and Macs have a similar character shortcut (well, sort of see, by trial and error, so i guess i can only prove a positive) I'm assuming that all of the people posting the Alt- stuff are Windows Users, since Macs don't have Alt, and there aren't many Linuxers out there.