Creation of this resource was inspired by a [url=http://www.gogeometry.com/problem/p287_regular_octagon_diagonal_ipad_sw_art_typography.htm]problem[/url] posted by [url=https://twitter.com/gogeometry]Antonio Gutierrez[/url]. [br][br]You can move the 2 LARGE WHITE POINTS anywhere you'd like at any time. [br][br][b]Key Questions:[br][br][/b]1) How do we know the octagon shown is a [b][color=#bf9000]regular octagon[/color][/b]? Explain.[br][br]2) Suppose each side of the octagon has length [i]a[/i]. How can we write the length of the [b][color=#9900ff]purple segment[/color][/b] as a [br] function of [i]a[/i]? That is, how can we write the length of the [b][color=#9900ff]purple segment [/color][/b]in terms of [i]a[/i]? [br][br]3) [b][color=#9900ff]How can we formally prove the phenomenon dynamically illustrated here? [/color][/b]