1 Cyclothymic Disorder, or Cyclothymiaâ a mild form of bipolar disorder. 2  People with cyclothymia have episodes of hypomania as well as mild depression for at least 2 years. 3  However, the symptoms do not meet the diagnostic requirements for any other type of bipolar disorder.
Shorter rulers are convenient for keeping in a pocket. Longer rulers, e.g., 18 inches (45 cm) are necessary in some cases. Rigid wooden or plastic yardsticks, 1 yard long and meter sticks, 1 meter long, are also used.
A sparse ruler is a ruler in which some of the distance marks may be missing. More abstractly, a sparse ruler of length L {\displaystyle L} with m {\displaystyle m} marks is a sequence of integers a 1 , a 2 , . . . , a m {\displaystyle a_{1},a_{2},...,a_{m}} where 0 = a 1 < a 2 < . . . < a m = L {\displaystyle 0=a_{1}<a_{2}<...<a_{m}=L} .