What's a convex taper?

So what exactly is a "convex" taper? Being relatively new to this craft, I seem to stumble around in conversations on the Rodmakers List with the mistaken impression that commonly used household terms have the same meaning in a bamboo rod shop. That's simply not the case. For example, a parabolic taper isn't really a parabola and stress curves are calculated for straight rods, not bent ones. Go figure.

My current state of confusion has to do with the term "convex". According to Wikipedia, convex means curving out or bulging outward...like a contact lens. That's also true of a bamboo taper, but...back in the day, someone named a certain type of taper Convex. In that context it means more than just convex. That particular type of taper has been explained in a book by Bill Harms and Tom Whittle (Split & Glued by Vincent C. Marinaro - see chapter 8). I'm oversimplifying, but what makes that particular type of taper a Convex taper is multiple convex sections between the tip top, ferrules and butt. Two Convex tapers are illustrated in the charts to the right (double click the image to view the charts). These are actual tapers from the book. The first taper has a full convex shape (the top left chart) and three convex sections (bottom left chart). The taper to the right has a linear full length taper and three convex sections. The full length shape of the taper has nothing to do with what Marinaro and others called a Convex taper. They were referring exclusively to a taper with multiple convex sections, no matter what the overall shape of the taper is. There's more to it than that, but that put's it in perspective. See the book for more detail.

I stumbled into the conversation several decades later. I'm looking at hundreds of tapers and trying to find some common characteristics that make similar tapers similar. Sounds simple enough, but the characteristic that emerged as that common denominator is the overall shape of the taper. I can group hundreds of tapers into common categories based on the overall shape of the tapers. In an attempt to avoid meaningless terms like parabolic, semi-parabolic and progressive, I simply called the different curves concave, linear and...you guessed it, CONVEX. But every time I use the term convex, someone points out that a convex taper isn't Convex unless it has multiple convex sections. I was baffled at first, but I understand the difference now.

I think I'll keep using the term convex to refer to the shape of a curve, not a particular taper. There are way to many confusing taper terms that could easily be explained using common household terms like concave, linear and convex. So if I say my rod is convex with a convex tip and a convex butt, you'll know exactly what I'm talking about. Or would it better to say it's a Convex Parabolic, or is that Parabolic Convex. I'm so confused!