in general. A similar calculation using the area of a circular sector gives 1 radian as 1 m2/m2. The key fact is that the radian is a dimensionless unit equal to 1. In SI 2019, the radian is defined accordingly as . It is a long-established practice in mathematics and across all areas of science to make use of . In 1993 the American Association of Physics Teachers Metric Committee specified that the radian should explicitly appear in quantities only when different numerical values would be obtained when other angle measures were used, such as in the quantities of angle measure (rad), angular speed (rad/s), angular acceleration (rad/s2), and torsional stiffness (N⋅m/rad), and not in the quantities of torque (N⋅m) and angular momentum (kg⋅m2/s). Giacomo Prando says "the current state of affairs leads inevitably to ghostly appearances and disappearances of the radian in the dimensional analysis of physical equations." For example, an object hanging by a string from a pulley will rise or drop by centimeters, where is the radius of the pulley in centimeters and is the angle the pulley turns in radians. When multiplying by the unit of radians disappears from the result. Similarly in the formula for the angular velocity of a rolling wheel, , radians appear in the units of but not on the right hand side. Anthony French calls this phenomenon "a perennial problem in the teaching of mechanics". Oberhofer says that the typical advice of ignoring radians during dimensional analysis and adding or removing radians in units according to convention and contextual knowledge is "pedagogically unsatisfying". At least a dozen scientists between 1936 and 2022 have made proposals to treat the radian as a base unit of measure defining its own dimension of "angle". Quincey's review of proposals outlines two classes of proposal. The first option changes the unit of a radius to meters per radian, but this is incompatible with dimensional analysis for the area of a circle, . The other option is to introduce a dimensional constant. According to Quincey this approach is "logically rigorous" compared to SI, but requires "the modification of many familiar mathematical and physical equations". In particular, Quincey identifies Torrens' proposal to introduce a constant equal to 1 inverse radian (1 rad−1) in a fashion similar to the introduction of the constant ε0. With this change the formula for the angle subtended at the center of a circle,