Why Geometer is not a Theorem Prover

• The drawing is only accurate to the resolution of your computer screen which is far less accurate than 1/100 centimeter—even on the best monitors available today. Maybe the lines just come close to meeting at a point—to within a billionth of a millimeter, for example.
• You only tried a few thousand examples. Maybe you missed the one bad one.
• The window on your computer screen is unlikely to be more than about 2000 pixels by 2000 pixels, and it's probably much smaller. What if the theorem starts to fail for triangles that are long and skinny—say 1,000,000 pixels long? (This reminds me of an exchange that occurred 30 years ago in a logic class taught by Fred Thompson at Caltech. A student was arguing with him about linguistics and (foolishly) said something about "a random English sentence". Professor Thompson said, "What do you mean by `a random sentence'?" The student grabbed a history text and said, "The fifteenth sentence on page 241 of this book." (or something like that). Thompson replied, "How on earth can you call that a random sentence? That book doesn't have even a single sentence with more than a million words in it, and almost all sentences are longer than that."