Abstract
This study was conducted to investigate how presenting two mathematical proofs of the Pythagorean theorem affects evaluating the beauty of the proofs. The authors conducted two experiments, each consisting of two sessions: a lecture on mathematical proofs of the Pythagorean theorem and evaluations of the beauty of the proofs of the theorem.
In Experiment 1, the subjects in Group D attended a lecture in which two proofs that most people view positively were explained and evaluated their beauty. The subjects in Group S attended a lecture in which one proof that most people view positively was explained and evaluated its beauty. The results demonstrated that the evaluation scores of the beauty in Group D were higher than those in Group S.
In Experiment 2, the proofs explained differed from Experiment 1, although the lecture and evaluations were the same. In Group D, two different proofs were explained: most people viewed one proof positively but not the other. In Group S only one proof, which was not viewed positively, was explained. The results showed that the evaluation scores of the beauty in Group D were lower than those in Group S.
The results in Experiments 1 and 2 suggest that the difference of presentation with two proofs of the Pythagorean theorem had two different effects: one is the “beauty raising effect” or the “beauty lowering effect” and the other is the “beauty-difference expanding effect”.
