﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.5953.21871"?>
<regions>
  <settings>
    <identity>
      <id>bd212f57-a3a8-432b-aa78-f69b8787195f</id>
      <revision>14</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.5953.21871" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Text Region" version="1.10.5953.21876" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Math Region" version="0.98.5953.21871" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
    </dependencies>
  </settings>
  <region id="0" left="63" top="0" width="238" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>MoscowLat:  55°45′36″N (55.760089)Long: 37°37′6″E (37.618467)</p>
    </text>
  </region>
  <region id="1" left="315" top="18" width="148" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">lat1</e>
        <e type="operand">55.760089</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="2" left="315" top="36" width="156" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">long1</e>
        <e type="operand">37.618467</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="3" left="63" top="63" width="242" height="56" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="rus">
      <p>KievLat:   50°28′12″N (50.469931)Long: 30°31′53″E (30.531317)</p>
    </text>
  </region>
  <region id="4" left="315" top="81" width="148" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">lat2</e>
        <e type="operand">50.469931</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="315" top="99" width="156" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">long2</e>
        <e type="operand">30.531317</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="6" left="63" top="126" width="63" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operand">1</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operand">60</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="7" left="135" top="126" width="63" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand" preserve="false" style="unit">″</e>
        <e type="operand">1</e>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operator" args="2">*</e>
        <e type="operand">60</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="8" left="63" top="171" width="303" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15" trailingZeros="true">
      <input>
        <e type="operand">55</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operand">45</e>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">36</e>
        <e type="operand" preserve="false" style="unit">″</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">55.760000000000000</e>
      </result>
    </math>
  </region>
  <region id="9" left="378" top="171" width="303" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15" trailingZeros="true">
      <input>
        <e type="operand">37</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operand">37</e>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">06</e>
        <e type="operand" preserve="false" style="unit">″</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">37.618333333333300</e>
      </result>
    </math>
  </region>
  <region id="10" left="63" top="198" width="303" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15" trailingZeros="true">
      <input>
        <e type="operand">50</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operand">28</e>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">12</e>
        <e type="operand" preserve="false" style="unit">″</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">50.470000000000000</e>
      </result>
    </math>
  </region>
  <region id="11" left="378" top="198" width="303" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15" trailingZeros="true">
      <input>
        <e type="operand">30</e>
        <e type="operand" style="unit">°</e>
        <e type="operator" args="2">*</e>
        <e type="operand">31</e>
        <e type="operand" preserve="false" style="unit">'</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operand">53</e>
        <e type="operand" preserve="false" style="unit">″</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
      </input>
      <contract>
        <e type="operand" style="unit">°</e>
      </contract>
      <result action="numeric">
        <e type="operand">30.531388888888900</e>
      </result>
    </math>
  </region>
  <region id="12" left="63" top="234" width="193" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">y</e>
        <e type="operand">x</e>
        <e type="function" args="2">atan2</e>
        <e type="operand">x</e>
        <e type="operand">i</e>
        <e type="operand">y</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="function" preserve="true" args="1">arg</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="63" top="288" width="222" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">dlat</e>
        <e type="operand">lat2</e>
        <e type="operand">lat1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">0.0923</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="14" left="63" top="324" width="246" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">dlong</e>
        <e type="operand">long2</e>
        <e type="operand">long1</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">0.1237</e>
        <e type="operator" args="1">-</e>
      </result>
    </math>
  </region>
  <region id="15" left="63" top="360" width="472" height="54" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">a</e>
        <e type="operand">dlat</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">lat1</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operand">lat2</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="operand">dlong</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">0.0035</e>
      </result>
    </math>
  </region>
  <region id="16" left="63" top="414" width="242" height="28" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">c</e>
        <e type="operand">2</e>
        <e type="operand">a</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operand">1</e>
        <e type="operand">a</e>
        <e type="operator" args="2">-</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="function" args="2">atan2</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">0.12</e>
      </result>
    </math>
  </region>
  <region id="17" left="63" top="441" width="173" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">radiusE</e>
        <e type="operand">6378135.0</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="18" left="63" top="459" width="173" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">radiusP</e>
        <e type="operand">6356750.0</e>
        <e type="operand" style="unit">m</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="19" left="63" top="477" width="390" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">nr</e>
        <e type="operand">radiusE</e>
        <e type="operand">radiusP</e>
        <e type="operator" args="2">*</e>
        <e type="operand">lat2</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">6.66</e>
        <e type="operand">10</e>
        <e type="operand">26</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">m</e>
        <e type="operand">4</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="20" left="63" top="531" width="493" height="37" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">dr</e>
        <e type="operand">radiusE</e>
        <e type="operand">lat1</e>
        <e type="function" preserve="true" args="1">cos</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operand">radiusP</e>
        <e type="operand">lat1</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="bracket">(</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">:</e>
      </input>
      <result action="numeric">
        <e type="operand">4.05</e>
        <e type="operand">10</e>
        <e type="operand">13</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand" style="unit">m</e>
        <e type="operand">2</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
      </result>
    </math>
  </region>
  <region id="21" left="63" top="585" width="203" height="43" color="#ff0000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2" exponentialThreshold="15">
      <input>
        <e type="operand">radius</e>
        <e type="operand">nr</e>
        <e type="operand">dr</e>
        <e type="operator" args="2">/</e>
        <e type="function" preserve="true" args="1">sqrt</e>
        <e type="operator" args="2">:</e>
      </input>
      <contract>
        <e type="operand" style="unit">km</e>
      </contract>
      <result action="numeric">
        <e type="operand">4055.25</e>
      </result>
    </math>
  </region>
  <region id="22" left="288" top="594" width="453" height="24" color="#000000" bgColor="#ff8080" fontSize="10">
    <text lang="eng">
      <p>As I mentioned, the source of this formula is unclear.</p>
    </text>
  </region>
  <region id="23" left="63" top="630" width="318" height="41" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">radius</e>
        <e type="operand">radiusE</e>
        <e type="operand">radiusP</e>
        <e type="operator" args="2">+</e>
        <e type="operand">2</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
      <contract>
        <e type="operand" style="unit">km</e>
      </contract>
      <result action="numeric">
        <e type="operand">6367.4425</e>
      </result>
    </math>
  </region>
  <region id="24" left="63" top="684" width="241" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2" exponentialThreshold="10">
      <input>
        <e type="operand">distance</e>
        <e type="operand">radius</e>
        <e type="operand">c</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">:</e>
      </input>
      <contract>
        <e type="operand" style="unit">km</e>
      </contract>
      <result action="numeric">
        <e type="operand">753.61</e>
      </result>
    </math>
  </region>
  <region id="25" left="63" top="720" width="208" height="24" color="#000000" bgColor="#ff8080" fontSize="10">
    <text lang="eng">
      <p>Yandex Maps gives 762 km</p>
    </text>
  </region>
  <region id="26" left="288" top="720" width="627" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <text lang="eng">
      <p>Wrong, measuring EXACTLY between these two points, Yandex Maps gives 755 km</p>
    </text>
  </region>
  <region id="27" left="351" top="747" width="169" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="2">
      <input>
        <e type="operand">c</e>
        <e type="operand">radiusE</e>
        <e type="operator" args="2">*</e>
      </input>
      <contract>
        <e type="operand" style="unit">km</e>
      </contract>
      <result action="numeric">
        <e type="operand">754.88</e>
      </result>
    </math>
  </region>
  <region id="28" left="63" top="756" width="194" height="41" color="#000000" bgColor="#ffffff" fontSize="10">
    <math>
      <input>
        <e type="operand">Ε</e>
        <e type="operand">1</e>
        <e type="operand">distance</e>
        <e type="operand">755</e>
        <e type="operand" style="unit">km</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
      <contract>
        <e type="operand" style="unit">%</e>
      </contract>
      <result action="numeric">
        <e type="operand">0.184</e>
      </result>
    </math>
  </region>
  <region id="29" left="63" top="810" width="232" height="24" color="#000000" bgColor="#ffff80" fontSize="10">
    <text lang="eng">
      <p>Google Maps gives 754.03 km</p>
    </text>
  </region>
  <region id="30" left="63" top="846" width="207" height="41" color="#000000" bgColor="#ffff80" fontSize="10">
    <math>
      <input>
        <e type="operand">Ε</e>
        <e type="operand">1</e>
        <e type="operand">distance</e>
        <e type="operand">754.03</e>
        <e type="operand" style="unit">km</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">-</e>
        <e type="operator" args="2">:</e>
      </input>
      <contract>
        <e type="operand" style="unit">%</e>
      </contract>
      <result action="numeric">
        <e type="operand">0.0555</e>
      </result>
    </math>
  </region>
</regions>