Summary
The video explores a notable error on a 1982 SAT question related to geometry and revolves around a concept known as the "coin rotation paradox." The question involved a problem where circle A rolls around circle B, with circle A's radius being one-third of circle B's.
Problem Overview: The problem asked how many revolutions circle A makes around circle B before returning to its starting point. The SAT offered multiple-choice answers, none of which were correct because the test writers made a mistake. They believed the answer was three, but the actual correct answer was four, which was not listed as an option.
Error Explanation: The error stems from a common misunderstanding about the way circles rotate around each other. When circle A rolls around circle B, it completes one additional rotation than expected due to the geometry involved. This is often misunderstood and is known as the "coin rotation paradox."
Student Correction: Three students, Shivan Kartha, Bruce Taub, and Doug Jungreis, identified the error and wrote to the College Board, proving that none of the provided answers were correct. The College Board admitted their mistake and nullified the question for all test takers.
Paradox and Mathematics: The video uses the coin rotation paradox to illustrate how objects rotate differently based on perspective and geometry. The presenter demonstrates that the circle completes an additional rotation when following a circular path due to the circumference involved.
Real-World Application: This concept also applies to timekeeping and astronomy, where differences in observed rotations affect how time is measured on Earth versus space. The video discusses sidereal time, used in astronomy to account for Earth’s rotation and orbit.
Implications and Impact: The SAT error had minor scoring implications for students, affecting their overall scores by a few points, but highlighted the importance of accurate problem-setting in standardized tests. The SAT is becoming less critical in college admissions, with many schools dropping standardized testing requirements post-COVID-19.
The video also includes a promotion for Brilliant, an educational platform offering interactive courses on science and mathematics.
And this is from 2007!