When we were dating, my wife had mentioned that she would want to use her Great-Grandmother's wedding band as her own. The wedding band is beautiful but I knew it would be difficult to find an engagement band that would pair nicely with it. Additionally, I didn't like the idea of simply buying what would be the most personal and intimate gift I would ever give. Therefore, I began a journey to design it myself using a combination of science, mathematics, and art.
I contacted Bario Neal Jewelry to help with fabrication and get and education on the practical constraints in jewelry design. I wanted a ring that would:
- Look good and fit with the wedding band
- Look good and fit with her finger during the engagement
- Have symbolic elements
I began by drawing the antique wedding band and an approximation of my wife's finger. I designed the engagement band slide around the wedding band with the finger locking them together. The engagement band sits with four contact points on the front of the wedding band keeping the stone about .7mm above the other ring. At the rear, the wedding band is lightly pinched by the two interwoven bands with a small detent. Throughout the engagement, the ring was worn alone and contacted the skin at four different locations on the front and with the two interwoven band in the rear.
While it initially appears to be four interwoven bands, the top two bands are actually part of the same path looped on itself. The bottom two bands are the same shape, but mirrored. In this way, the engagement ring is actually two interwoven bands. The initial design was performed in Mathematica by expressing the path as a function represented by a trigonometric series with unknown coefficients. I then put in a series of constraints on f(x) and f'(x) at various locations to specify intersection points for structural integrity and to hold the stone. I then solved for the series coefficients by minimizing the average width of the ring.
The design was then fabricated on a rapid-protyping machine to create a wax-positive which was cast to create a brass positive, and then ultimately the ring itself.