I have a ArcGIS service configured as shown in this pastbin. Specifically, the first LOD looks like this:
{
"level": 0,
"resolution": 222.2222222222222,
"scale": 256000
}
I determined how to convert from the scale of 256000 to arrive at a resolution of 222.222:
var dotsPerInch = 96.0;
var inchesPerFoot = 12.0;
var dotsPerUnit = dotsPerInch * inchesPerFoot;
var scale = 256000;
var resolution = scale / dotsPerUnit;
But the associated WMTS service reports a "ScaleDenominator" value of 241904.7619047619:
<TileMatrix>
<ows:Identifier>0</ows:Identifier>
<ScaleDenominator>241904.7619047619</ScaleDenominator>
<TopLeftCorner>-1.77905E7 4.643889999999999E7</TopLeftCorner>
<TileWidth>256</TileWidth>
<TileHeight>256</TileHeight>
<MatrixWidth>3</MatrixWidth>
<MatrixHeight>3</MatrixHeight>
</TileMatrix>
What are the mathematics behind this value? That is, given a scale of 256000 how did ESRI arrive at a ScaleDenominator of 241904.7619?