Treadmills (TM) and elliptical devices (EL) are popular forms of exercise equipment. The differences in the training stimulus presented by TM or EL are unknown. The purpose of this investigation was to evaluate oxygen consumption, energy expenditure, and heart rate on a TM or EL when persons exercise at the same perceived level of exertion. After measuring peak oxygen uptake (VO2peak) in 9 male and 9 female untrained college-aged participants, the subjects performed 2 separate 15-minute submaximal exercise tests on the TM and EL at a rating of perceived exertion (RPE) of 12-13. VO2peak was higher (p<0.05) in the males (48.6+/-1.5 vs. 45.2+/-1.6 ml/kg/min) than the females (41.7+/-1.8 vs. 38.8+/-2.2 ml/kg/min) for both TM and EL (means+/-standard error of the mean; for TM vs. EL respectively), but there were no differences in the measured VO2peak between TM or EL. During submaximal exercise there were no differences in RPE between TM and EL. Total oxygen consumption was higher (p<0.05) in males (30.8+/-2.2 vs. 34.9+/-2.2 L) than females (24.1+/-1.8 vs. 26.9+/-1.7 L) but did not differ between TM and EL. Energy expenditure was not different between TM (569+/-110 J) or EL (636+/-120 kJ). Heart rate was higher (p<0.05) on the EL (164+/-16 beats/min) compared to the TM (145+/-15 beats/min). When subjects exercise at the same RPE on TM or EL, oxygen consumption and energy expenditure are similar in spite of a higher heart rate on the EL. These data indicate that during cross training or noncompetition-specific exercise, an elliptical device is an acceptable alternative to a treadmill.

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We present a method for automatically building diagrams for olympiad-level geometry problems and implement our approach in a new open-source software tool, the Geometry Model Builder (GMB). Central to our method is a new domain-specific language, the Geometry Model-Building Language (GMBL), for specifying geometry problems along with additional metadata useful for building diagrams. A GMBL program specifies (1) how to parameterize geometric objects (or sets of geometric objects) and initialize these parameterized quantities, (2) which quantities to compute directly from other quantities, and (3) additional constraints to accumulate into a (differentiable) loss function. A GMBL program induces a (usually) tractable numerical optimization problem whose solutions correspond to diagrams of the original problem statement, and that we can solve reliably using gradient descent. Of the 39 geometry problems since 2000 appearing in the International Mathematical Olympiad, 36 can be expressed in our logic and our system can produce diagrams for 94% of them on average. To the best of our knowledge, our method is the first in automated geometry diagram construction to generate models for such complex problems.

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