======Using Mathematics to Estimate a Quantity of Interest such as "How Big is the Sun?"====== Students drew ray diagrams and used prior knowledge of geometry of similar triangles to calculate the diameter of the sun: |{{days:fall2012daybyday:fall2012day3:s6300628.jpg?500x500}}| |{{days:fall2012daybyday:fall2012day3:s6300629.jpg?500x500}}| Variables Used: * H= diameter of the sun * h= diameter of the image of the sun * D= distance from the sun to the pinhole * d= distance from the pinhole to the image Geometry of similar triangles: ratios of height to distance to pinhole are equal * H/D=h/d * H= (D)(h)/(d) * (100,000,000 miles)(1 cm)/(100cm)= about 1,000,000 miles