## [12]Annulene and Two Simple Derivatives – Aromaticity?

Complex chemicals possess names almost equally complex. Occasionally, a simpler nomenclature can be employed. For basic aromatic compounds, composed of a ring of alternating single and double bonded carbon atoms in a ring, the name [n]annulene has been is commonly used. Examples, including [12]annulene are given below. Aromaticity We won't go into the theory behind aromaticity. What we will do is lay out the basic factors that students use to determine if a compound is aromatic. 1. The ring is composed of conjugated single and double bonds (...−C=C−C=...). 2. The molecule is relatively flat. 3. The number of available π-electrons equals 4n + 2 (a Hückel number), where n is generally a small positive integer.¹ 4. Crowding does not severely limit or prevent aromaticity. 5. Ring size affects aromaticity, but…

## Introduction to Cylindrical Coordinates

What are cylindrical coordinates? A coordinate system is a system that provides a way to describe points and other features of geometric figures in Euclidean space. Generally the best coordinate system is that system which adequately does the job in simplest fashion. In this article, we will use (r, Φ, z) for our new coordinate system. Many use this, but others use a different assortment of letters, unfortunately. Forewarned is forearmed. Cylindrical Coordinates - Introspection When we're working in two dimension, we are able to draw our coordinate axes using the sheet of the paper, representing a plane. Two orthogonal axes are drawn, one horizontal the other vertical. When using r and Φ the way we view the axes is really different from how we view them when they represent x…