# Transverse Mercator Projection

A conformal cylindrical projection: The transverse aspect of Mercator projection. Also known as Gauss Conformal (ellipsoidal form only), Gauss-Kruger (ellipsoidal form only) and Transverse Cylindrical Orthomorphic. Shown greatly zoomed in since profound distortion occurs outside the target region.

###### Limitations

The accuracy of Transverse Mercator projections quickly decreases from the central meridian. Therefore, it is strongly recommended to restrict the longitudinal extent of the projected region to +/- 10 degrees from the central meridian. [The US Army standard allows +/- 24 degrees from the central meridian].

This requirement is met within all State Plane zones that use Transverse Mercator projections.

###### Scale

True along the central meridian or along two straight lines on the map equidistant from and parallel to the central meridian. Scale is constant along any straight line on the map parallel to the central meridian. These lines are only approximately straight for the projection of the ellipsoid, and will be the case within Manifold when ellipsoidal Earth models (the standards) are used.

Scale increases with distance from the central meridian, and becomes infinite 90° from the central meridian.

###### Distortion

Infinitesimally small circles of equal size on the globe appear as circles on the map (indicating conformality) but increase in size away from the central meridian (indicating area distortion).

###### Usage

Many of the topographic and planimetric map quadrangles throughout the world at scales of 1:24,000 to 1:250,000. Basis for the Universal Transverse Mercator (UTM) grid and projection. Basis for the State Plane Coordinate System in U.S. States having predominantly north-south extent. Recommended for conformal mapping of regions having predominantly north-south extent.

###### Origin

Presented by Johann Heinrich Lambert (1728 - 1777) of Alsace in 1772. Formulas for ellipsoidal use developed by Carl Friedrich Gauss of Germany in 1822 and by L. Kruger of Germany, L.P. Lee of New Zealand, and others in the 20th Century.

###### Carl Friedrich Gauss (1777 - 1855)

Born Johann Carl Friedrich Gauss, one of the greatest mathematicians who has ever lived.  Despite his profound abilities in mathematics, Gauss doubted he could earn a steady living as a mathematician and became a professional astronomer, taking a life-long post as the director of the observatory in Gottingen.   Gauss was the first to develop the Fast Fourier transform (as a trigonometric interpolation method), revolutionized orbital computations and invented the theorem proving the curvature of a surface can be determined entirely by measuring angles and distances on the surface.   Late in life he revolutionized electromagnetism with Gauss's Law, that the total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity, and revolutionized optics with the Gaussian lens formula.

###### Options

Specifying latitude origin and longitude origin centers the map projection.