The simplest solution to the tautochrone problem is to note a direct relation between the angle of an incline and the gravity felt by a particle on the incline. A particle on a 90° vertical incline undergoes full gravitational acceleration g , while a particle on a horizontal plane undergoes zero gravitational acceleration. At intermediate angles, the acceleration due to "virtual gravity" by the particle is g sin ⁡ ⁡ θ θ . Note that θ θ is measured between the tangent to the curve and the horizontal, with angles above the horizontal being treated as positive angles. Thus, θ θ varies from − − π π / 2 to π π / 2 .