  To measure the properties of both components of the RS CVn binary sigma
Geminorum (sigma Gem), we directly detect the faint companion, measure the
orbit, obtain model-independent masses and evolutionary histories, detect
ellipsoidal variations of the primary caused by the gravity of the companion,
and measure gravity darkening. We detect the companion with interferometric
observations obtained with the Michigan InfraRed Combiner (MIRC) at Georgia
State University's Center for High Angular Resolution Astronomy (CHARA) Array
with a primary-to-secondary H-band flux ratio of 270+/-70. A radial velocity
curve of the companion was obtained with spectra from the Tillinghast Reflector
Echelle Spectrograph (TRES) on the 1.5-m Tillinghast Reflector at Fred Lawrence
Whipple Observatory (FLWO). We additionally use new observations from the
Tennessee State University Automated Spectroscopic and Photometric Telescopes
(AST and APT, respectively). From our orbit, we determine model-independent
masses of the components (M_1 = 1.28 +/- 0.07 M_Sun, M_2 = 0.73 +/- 0.03
M_Sun), and estimate a system age of 5 -/+ 1 Gyr. An average of the 27-year APT
light curve of sigma Gem folded over the orbital period (P = 19.6027 +/- 0.0005
days) reveals a quasi-sinusoidal signature, which has previously been
attributed to active longitudes 180 deg apart on the surface of sigma Gem. With
the component masses, diameters, and orbit, we find that the predicted light
curve for ellipsoidal variations due to the primary star partially filling its
Roche lobe potential matches well with the observed average light curve,
offering a compelling alternative explanation to the active longitudes
hypothesis. Measuring gravity darkening from the light curve gives beta < 0.1,
a value slightly lower than that expected from recent theory.
