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Famous Theorems

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theorem00 The concept of "Famous Theorems"
theorem01 Theorem of Morley
Exproring feature



Content of theorem


theorem02 Mid points theorem
Content of theorem



Understaing with track



Understanding with measurement

Let's move point A. What do you find? L...



Clue for proof



Related figure


theorem03 Theorem of incribed angles
Special case



Combination of special cases



Understanding with measurement



Understanding with the other cases


theorem04 Pythagolean theorem
Conjecture



Measurement (Area of squares)



measurement (Length of sides)



Euclidean additional line and measurement



Euclidean additional line and "which case the relationship does not exist"



Congruence of triangles


theorem05 Pappus' theorem
theorem06 方べきの定理
Transformation and conjecture



Measurement and conjecture



Specialize and conjecture



Confirm



Triangle and proof (1)



Generalization and clasification



Triangle and proof (2)



Triangle and proof (3)


theorem07 Simson's theorem
What is the feature



Confirm the different cases



See as the relationship between three points



See as the transformation of triangle



See as the change of the area of triangle



Maximum of the area of triangle



Area of triangle and circumcenter



Area of triangle and circle


theorem08 Menelaus' theorem
Observation and conjecture



Observation and confirm



Observation


theorem09 Cheva's theorem
Observation and conjecture



Observation and confirm



Observation


theorem10 Desargues' theorem
Observation and conjecture



Secret of three points



Relationship of three points



Different cases


theorem11 Euler line
Observation and conjecture



Observation and conjecture



Observation and conjecture


theorem12 Newton's theorem (Newton's line)
Observation and conjecture



Observation and conjecture


theorem13 Newton's theorem
Observation and conjecture



Observation and conjecture


theorem14 Pappus' theorem
Observation and conjecture



Observation and conjecture



Observation and conjecture



This is not enough


theorem15 Pascal's theorem
Observation and conjecture



Observation and conjecture



Observation and conjecture



This is not enough


theorem16 Feuerbach's theorem
Four circles



This circle



Feature of circle (1): Three points circle



Feature of circle (2): Three points circle



Six points circle



Nine points circle



Forum of Gemetric Constructor by Y.Iijima