# Donkey bridges

 A memnonic game which allows connections between different ideas is called a donkey bridge. The word probably diffused into the English as a translation from the German "Eselsbrücke". They appear in any language. In German there is the bridge to remember whether the moon is increasing or decreasing. Z for "zunehmend=increasing" matches the crescent moon and A for "abnehmend=decreasing" matches the shrinking moon. In French, there is the "stalacTites" for "tomber=Falling" and "stalagMites" for "monter=raise". Here are examples in calculus. The third example inflates the name to make it memorable. It is a bridge in a wider sense. If you should know bridges for calculus formulas, let me know.
 SOHCAHTOA Sin Opposite/Hypothenuse, Cos Adjacent/Hypothenuse, Tan Opposite/Adjacent This is a classic. The word matches an island. Wikipedia knows an other one: "Some Old Horses Chew Apples Happily Throughout Old Age". Low D High take High D Low - Cross the line and square the Low Quotient rule I learned this from Inanna, a student in the class. lim sin(t)/t =1 the fundamental theorem of trigonometry. I learned the name "fundamental theorem" from Otto Bretscher. It can not be stressed enough how important the limit is. We have seen in class that we can use this limit to get the derivatives of all trig functions at every point. It is also a "prototype limit". If you understand this limit, you understand almost every other limit too. The function sin(t)/t appears in lots of places and its justified to call the function sinc(x) = sin(x)/x with its own 4 letter name.
 LIPET This encodes the order for integration by parts: Logarithms, inverse trig functions, powers, exponentials and trig functions. Use this memnonic device if you are a tea lover (Lipton). LIATE This is an other memnonic to remember the order: Logarithms, inverse trig functions, algebraic functions, Trig functions and exponentials. Use this memnonic device if you are a coffee lover (Latte). ALL STUDENTS TAKE CALCULUS reminds about the sign of trig functions in the 4 quadrants. In the first quadrant, all are positive, in the second, only sin is positive, in the third only tan is positive and in the fourth, only cos is positive. Added, October 30, 2011 (Thanks to Tracy): THE "C"S DON'T GO TOGETHER. To remind that sec=1/cos and csc = 1/sin. Added, October 30, 2011 (Thanks to Jason Zhang):