Constructing a Pentagon (with a compass) 

I always try to figure out why a math equation/theorem works. A regular pentagon has a ton of math ideas built into it!

Glad it was helpful, and I am glad you appreciated the background information! This construction is a lot of fun, even though it is complicated. Best wishes with geometry!

@@vinteachesmath Thanks for the reply. Curious how I came to find your video. I'm a Waldorf teacher and have used this construction a few times to teach children to make 11 piece star lanterns for mid winter festivals in Zimbabwe and South Africa. Suddenly find myself needing to do this again with a group of 12 year olds. Cannot find my book with instructions. No other teachers have recollection of where the other copy is. Then I looked online but found inadequate help until...

Glad to hear that!

Glad to hear that!

You’re welcome 😊

I am glad you enjoyed the video. Even though we do not require 10th graders to construct pentagons anymore, I still think it is a fascinating piece of math. I like your question! I would say it depends on the value of the angle they want you to construct. Unless you are starting with the base angle on the side as well as the line segments needed to build the exact perimeter. I remember reading somewhere else that there are some constructions that have over 100 steps. As you look at polygons with more sides, the steps of the construction increase. Truly awesome that some people figured all this stuff out!

@@vinteachesmath Lay out the perimeter (AB). Measure the the base angle and construct it at A and at B to create a "giant" isosceles triangle. They the two lines intersect at C. Bisect angles A and B. The bisectors intersect at D. Measure Angle DAB and construct it at D on segments AD and BD. Where the angles intersect AB, you've created intersections E and F. ADE and DFB are isosceles triangles. Hence, AE = ED = DF = BF. Hence DEF is a triangle with a perimeter equal to AB. AB = AE + EF + FB or AB = DE + EF + BF. If are curious for additional proof, AEF is 180° angle, Angle AED = 180° - 2 x DAE (which is half the base angle CAB. Hence Angle DEF = base angle.

nerd

I don't know if there is a specific name for this technique, but this construction uses the concept of the Golden Ratio. As we add more sides to the polygon, the constructions only get more complicated!