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Below is the source input I used for this validation:

  1. <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
  2. "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
  3. <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" lang="en"><head>
  4. <meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
  5. <meta name="Author" lang="en" content="Miguel Casquilho" />
  6. <title>M&middot;C, IST: tangent, error</title>
  7. <link rel="stylesheet" type="text/css"
  8. href="http://web.tecnico.ulisboa.pt/~mcasquilho/commonstyle.css" />
  9. <style type="text/css">
  10. .divx {font-size: 10pt; margin-left: 0.25in; text-indent: -0.25in}
  11. a.special:hover {color: inherit; background-color: aqua}
  12. .pt {color: #ff00ff; background-color: transparent} </style>
  13. </head> <!--11Sep2010 MC-->
  14. <body class="sm">
  15. <form method="post" action=
  16. "http://web.tecnico.ulisboa.pt/~mcasquilho/cgi-bin/interface_png.php?errtangent">
  17. <input name="executable" type="hidden" value="errtangent.exe" />
  18. <table width="90%" bgcolor="#eeeeee" align="center" border="1" class="sm">
  19. <tr><td colspan="3">
  20. <table width="100%" class="sm">
  21. <tr><td width="50px"><a href='https://fenix.ist.utl.pt/departamentos/deq'><img alt='&copy;'
  22. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/MC.gif" border='0'
  23. width='40' height='41' /></a>
  24. </td><!--title-->
  25. <td><div style="font-size: 13.5pt; text-align: center"><!-- title --><b
  26. onmouseout="this.style.color='blue', this.style.fontStyle='normal'"
  27. onmouseover="this.style.color='red',
  28. this.style.fontStyle='bold'">
  29. Tangent:
  30. error in angle</b></div>&emsp;
  31. Finds (via Monte Carlo) the error in an angle from its tangent.<!--b>
  32. UNDER&nbsp;CONSTRUCTION</b--></td>
  33. <td width="112px"><table width='100%'>
  34. <tr><td align='center' bgcolor='white'>
  35. <input type="submit"
  36. value="&nbsp; Execute &nbsp;" style="background-color: #00bfff"
  37. onmouseout="this.style.fontStyle='normal', this.style.fontWeight='normal'"
  38. onmouseover="this.style.fontStyle='normal', this.style.fontWeight='bold'" /></td>
  39. </tr><tr><td align='center'><span style='font-size:
  40. xx-small'>2021.Mar.16 03:49:52</span></td></tr>
  41. </table>
  42. </td></tr>
  43. </table> </td></tr><!-- ...................................... -->
  45. <tr><td width="15%" align="center">Height, <i>h</i>:&nbsp;
  46. <i>&mu;</i>, <i>&delta;</i></td>
  47. <td width="45%"><input name="nvar" type="hidden"
  48. value="2" /><input name="hmu" type="text" value="11.3" size="5"
  49. maxlength="8" /><input name="hdel" type="text" value="1." size="5"
  50. maxlength="8" /></td>
  51. <td width="40%"><i>Height</i> of right-angled triangle
  52. ("opposite" leg).</td></tr>
  54. <tr><td align="center">Base, <i>b</i>:&nbsp;
  55. <i>&mu;</i>, <i>&delta;</i></td>
  56. <td><input name="bmu" type="text" value="25" size="5"
  57. maxlength="8" /><input name="bdel" type="text" value="1." size="5"
  58. maxlength="8" /></td>
  59. <td><i>Base</i> of right-angled triangle ("adjacent" leg). &bull;</td></tr>
  61. <tr><td align="center">Pr(<i>&mu;</i> &plusmn; <i>&delta;</i>)</td>
  62. <td><input name="prob" type="text" value="95.45" size="5"
  63. maxlength="8" /> % &emsp; (2<i>&sigma;</i>: 95.45 %,
  64. 3<i>&sigma;</i>: 99.73 %)</td>
  65. <td>Assigned <i>probability</i> for interval. &bull;</td></tr>
  67. <tr><td align="center">Graph</td>
  68. <td><select name="igraf"><option value="1">indV</option><option
  69. value="2" selected="selected">angle</option></select></td>
  70. <td>Graph: independent var.s (<i>h</i>, <i>b</i>),
  71. angle (<i>&beta;</i>). &bull;</td></tr>
  73. <tr><td align="center"><i>N</i>, .seed</td>
  74. <td><select name="ntrials"><option value="1500">1 500</option><option
  75. value="40000" selected="selected">40 000</option><option
  76. value="1000000">1 million</option><!-- option
  77. value="25000000">25 M</option --></select>(M, million) <input name="iseed"
  78. type="text" value="0" size="5" maxlength="8" /></td>
  79. <td>No. of <i>trials</i>, random <i>seed</i>. &bull;</td></tr>
  81. <tr><td align="center">tol, klass, <i>y</i><sub>max</sub></td>
  82. <td><input name="tol" type="text" value="1.-6" size="4"
  83. maxlength="8" /><select name="klass"><option
  84. value="200" selected="selected">200</option><option
  85. value="625">625</option></select><input name="ymax" type="text"
  86. value="0" size="5" maxlength="8" /> &emsp; ['0' (&not; '.0'), auto.]</td>
  87. <td><i>Tolerance</i>, no. of histo. <i>classes</i>,
  88. max. <i>y</i> for graph. &bull;</td></tr>
  90. <!-- tr><td align="center"><i>x</i><sub>0</sub>, <i>x<sub>n</sub></i></td>
  91. <td><input name="x0" type="text" value="490" size="6"
  92. maxlength="8" /><input name="xn" type="text" value="515" size="6"
  93. maxlength="8" /> g</td>
  94. <td>Extreme <i>x</i>'s for graph. &bull;</td></tr -->
  96. <tr><td align="center">Show values</td>
  97. <td><select name="ishow"><option value="0" selected="selected">No</option>
  98. <option value="1">Yes</option></select></td>
  99. <td>Shows the coordinates of the graph. &bull;</td></tr>
  101. <!-- plot gnudata.dat \ (or anything: this line is a MANDATORY dummy) -->
  103. <tr><td colspan="3"><input name="gnuplot" type="hidden"
  104. value="set term png enhanced font '/usr/share/fonts/truetype/freefont/FreeSerif.ttf' 13
  105. set timestamp 0, -1. '/usr/X11R6/lib/X11/fonts/Type1/parkave.pfb'
  106. set size 0.85, 0.85; set nokey
  107. set title 'Tangent: error in angle' -2, +.5
  108. set xlabel 'h, b --- or beta' 12, .6; set ylabel 'pdf'
  109. set yrange [0:*]
  110. #set y2label 'F(x)'; set ytics nomirror; set y2range [0:1]; set y2tics .2
  111. plot anyname.dat \
  112. usi 1:2 with lines linetype 1 linewidth 3, \
  113. '' usi 1:3 with lines linetype 2 linewidth 3" /><p class="ij">Finds the value and error of
  114. the angle, <i>&beta;</i>, in a right-angled triangle, such that
  115. tan&nbsp;<i>&beta;</i>&nbsp;=&nbsp;<i>h</i>&nbsp;&frasl;&nbsp;<i>b</i>,
  116. from the measurement of its height, <i>h</i>
  117. &mdash;the <i>leg</i> (or <i>cathetus</i>) opposite to the angle&mdash;
  118. and its base, <i>b</i> &mdash;the leg adjacent to the angle&mdash;,
  119. hence, <i>&beta;</i>&nbsp;=&nbsp;arctan(<i>h</i>&nbsp;&frasl;&nbsp;<i>b</i>).</p>
  121. <p class="ij">The method is Monte Carlo simulation. The
  122. <a href="./,Gauss/ErrorTangent.pdf">theoretical result</a>.<i>pdf</i>,
  123. also given, is: <i>&delta;&beta;</i> = (sin<i>&beta;</i>)(cos<i>&beta;</i>)
  124. &radic;[<i>&epsilon;</i>&sup2;(<i>h</i>) + <i>&epsilon;</i>&sup2;(<i>b</i>)].
  125. Thus, the theoretical and simulated results can be compared.</p>
  127. <p class="ij">(The <i>tolerance</i> is for the numerical inversion of
  128. the Gaussian distribution.)</p>
  130. <p class="ij">Graphs are shown for the behaviour of:
  131. the independent (Gaussian) variables (<i>h</i> and <i>b</i>); or
  132. the dependent variable (<i>&beta;</i>).
  133. Note that the distribution of <i>&beta;</i> is not Gaussian
  134. (though possibly approximately so).</p></td></tr>
  136. <tr><td align="center"><input type="reset" style="font-size: smaller"
  137. value=" Reset " /></td><td><i>References:</i></td>
  138. <td align="center">Plate: ErrorTangentAngle</td></tr>
  139. <tr><td colspan="3"><p class="ref">&bull;&nbsp;<span
  140. class="sc">Taylor</span>, 1997 (see Bibliography), or Nepf (already cited).</p>
  142. <p class="ref">&bull;&nbsp;1623-09-11: <a href=
  143. "http://www-groups.dcs.st-and.ac.uk/~history/Biographies/Angeli.html"
  144. ><span class="sc">Angeli</span></a>, Stefano degli, or 21.st of Sep.
  145. (1697-10-11).</p></td></tr>
  146. </table>
  147. </form>
  149. <div style="line-height: 6pt">&nbsp;</div>
  150. <div style="line-height: 1.5pt; color: black;
  151. background-color: red">&nbsp;</div>
  153. <table width="100%" class="sm"><tr>
  154. <td width="58px"><a href="http://validator.w3.org/check?uri=
  155. http://web.tecnico.ulisboa.pt/~mcasquilho/compute/qc/Fx-errtangent.php;verbose=1;ss=1"><img
  156. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/valid-xhtml10s.png"
  157. alt="Valid HTML 4.01!" border="0" width="55px" height="19px" /></a></td>
  158. <td width="15%" align="left"><a href="http://www.tecnico.ulisboa.pt"><img
  159. src="http://web.tecnico.ulisboa.pt/~mcasquilho/depot/wwwist.png"
  160. alt="IST" align="middle" border="0" width="88px" height="34px" /></a></td>
  161. <td width="70%" align=
  162. "right"><i>http://web.tecnico.ulisboa.pt/~mcasquilho/compute/qc/Fx-errtangent.php</i><br />
  163. <i>Created:</i> 2010-09-11 &mdash; <i>Last modified:</i> 2010-09-14</td></tr></table>
  164. </body></html>

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