Some pencils are round but most of them seem to be hexagonal.
A hexagonal is more comfortable to use, easier to make, and harder to roll off a table. Personally I find pencils too thin to hold with any comfort so I like to put a kind of rubber tube around the waist of the pencil.
Of course the very first pencil sharpeners were knives and blades, but the first patent for a tool especially for sharpening pencils was made by Bernard Lassimone, a French mathematician, in 1828. It looked something like this:
However the first mechanical pencil sharpener was invented by Therry des Estwaux, also from France in 1847. It looked something like this:
Now there are sharpeners with revolving handles, and even battery operated electric sharpeners, but I like the simple wooden ones like this:
Mechanical pencil? Propelling pencil? In Japan most of my students call it a Sharp pencil.
This type of pencil was invented in Britain in 1822 by Sampson Mordan and Gabriel Riddle.
The mechanical pencil became popular in Japan and in 1915 Tokuji Hayakawa first made the type of mechanical pencil that is still used today. He called it the Ever Ready Sharp Pencil.
At first sales were small, but after a few years sales suddenly boomed. Hayakawa started a company which he named Sharp. This is the origin of the world-famous electronics company which now makes everything from fridges to Aquos TVs.
The first people to make wooden holders for black graphite pencils were an Italian couple, Simonio and Lyndiana Bernacotti, sometime around 1560. They were carpenters and they used juniper wood to make a compact, flat pencil.
Shortly after a better way was found using two semi-circles of wood, which were glued together. This is basically the same method that is still used today. The two methods are shown in the drawings below.