[QuesnayJr]

You can give a function that maps the points of the triangle to the points of the circle in such a way that this function is continuous. (Continuous basically means "no jumps".)

You can give this function explicitly. Let's assume that the triangle is drawn on a piece of paper with an x and y axis, such that the intersection of the axes (the origin) is inside the triangle. For each point on the triangle, draw a line from the origin to the point. Take the angle between that line and the x-axis. Use that angle to map it onto a circle.