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The scale factor along at the origin (the poles) is adjusted to cut back the overall distortion of scale inside the mapped region. Similarly to the Mercator projection, the vicinity near the tangent (or secant) point on the Stereographic map remains very close to true scale on an angular distance of some degrees. On the ellipsoidal model, a stereographic projection tangent to your pole have a scale factor of not as much as 1.003 at 84 latitude and 1.008 at 80 latitude.
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