You are probably wondering why I'm writing about expensive pens in a math column? Believe it or not, these pens are interesting from a mathematical point of view.

The other thing about these three pens is they are not your standard pens. They are fountain pens which have 18 carat nibs and can be refilled with ink but at these prices, I don't think I'd use them.

The first pen was built using a practical application of math in its creation. One, we don't usually think about.

This pen, Fulgor Nocturnus Pen created by Tibaldi of Florence Italy, sold for $8 million dollars back in 2010 at an action in China.

So what made it capture my attention? It was created using based on the Divine Proportions of Phi also known as the golden ratio or 1.618. The ratio between the cap and the visible barrel with the closed cap is a perfect 1.618. The pen is decorated with 925 black diamonds and 123 rubies.

Several other expensive pens in the $200,000 to $500,000 range are not your usually cylindrical shape. They have hexagonal or 6 sided barrels. One is the Gotica pen with a beautifully decorated barrel encrusted with 892 diamonds, 72 rubies, and 72 rubies costing just over $400,000, while another is the La Modinista pen with 5,072 diamonds and 96 rubies on the hexagonal barrel for only $250,000.

It might be interesting to have students design a pen using the golden ratio just as the Fulgor Nocturnus.

Let me know what you think. I found this rather intriguing that pens can be created using the golden ratio.