In 1885, Adolf von Baeyer published a paper on polyacetylene compounds in the journal of the German Chemical Society. At the end of the paper, a discussion appeared on the strain in small ring compounds. Baeyer reasoned that since the bond angle in a perfect tetrahedron (the tetrahedral carbon had been proposed independently by van't Hoff and LeBel in 1874) is 109o 28' [109 degrees, 28 minutes; (1o = 60 ')], then the amount of strain in a small ring compound would be the half the difference between the tetrahedral value and the internal angle of a regular polygon. Why half? Because the strain would be distributed equally to "each bond" connected to a carbon.
Baeyer considered ethylene to be a special polygon with an internal angle of 0o, thus its value of +54o 44'. The internal angle of the equilateral triangle (cyclopropane) is 60o and for a square (cyclobutane) is 90o. Try the calculation. What is the internal angle of a regular pentagon or hexagon? The sum of all supplementary angles about any polygon is equal to 360o. Thus, the supplementary angle for each internal angle of a regular hexagon is 120o. Do the calculation for each of these cyclic hydrocarbons. You can see why Baeyer reached the conclusion that cyclopentane, with its minimum value, is less strained than cyclohexane. Although Baeyer used the value 109o 28' for the tetrahedral carbon, he nonetheless viewed the cycloalkanes as planar species. He reasoned that the equatorial and axial positions on cyclohexane would be unique. Thus, there should be an axial cyclohexanecarboxylic acid and an equatorial one. Of course, with the benefit of over 100 years of hindsight, we realize that these two carboxylic acids interconvert rapidly at ambient temperature! [Note: The value for cyclobutane should be 9o 44'.]