My experience is that you cannot argue certain things that are pushed off the table with blank disclaimers.
- Photos of the round earth or other space-based evidence is dismissed as a "NASA/UN conspiracy" - you can't prove that it's not a conspiracy - so it's really not worth the effort to try. This evidence is "off the table".
- Scientific results and similar things are dismissed as "Have YOU actually TRIED that?" - and since you don't happen to have a handy 100" telescope in your back yard - you're not going to win that argument either.
[li]Things that require too much math or trigonometry don't work well because most FE'ers get lost in the weeds of the math - so right or wrong, the results are not compelling.
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HOWEVER: The most compelling evidence are simple observations that anyone can make. How do sunsets happen? How does the moon have phases? Why does a new moon look 'vertical' in the north, 'horizontal' at the equator and 'upside-down' in the southern parts of the planet? How is it that Quantas can fly you from Australia to South America or South Africa when the Flat Earth map of the world shows that these distances are more than twice the range of a 747 airliner and the flight times would require them to fly at twice the speed of sound? Why are there TWO high tides and TWO low tides every day?
These questions are VERY tough for Flat Earth people to answer - they are not easily dismissed - and the evidence is ridiculously easy to find.
So look for simple stuff - and stick within the rules of evidence that your friend is willing to accept. This is a fascinating intellectual exercise.
I doubt you'll convince him/her though.