Ask any fifth-grader what the angles of a triangle add up to, and she’ll say: ‘180 degrees’. That isn’t true on a hyperbolic surface. Ask our fifth-grader what’s the circumference of a circle and she’ll say: ‘2π times the radius’.
I don't remember learning plane geometry in 5th grade. Maybe times have changed
I remember my sixth grade teacher getting all the students to make triangles and measure the total of the inside angles. I was so annoyed by my classmates all getting near to 180 degrees, they just seemed like a bunch of boring conformists. I went out of my way to construct a triangle with 150 degrees internal angle, which I was quite proud of at the time. And thus began my career as a mathematical weirdo.
I don't remember learning plane geometry in 5th grade. Maybe times have changed