Finding the Area of a Circle
Students often wonder where the formula for the area of a circle comes from; and knowing something about that can help make it more memorable, as I discussed previously about other basic area formulas.
Formulas
Principles for Solving a Formula
(An archive question of the week) Last time I discussed issues that arise in solving a simple algebraic equation. In researching that, I found a discussion of solving a formula for a variable (which in some countries is called “making x the subject”, that is, changing an equation involving x into the form “x = …
Is Area of a Square a Circular Argument?
(New Question of the Week) I love it when students want to know why something has to be the way it is, and are not satisfied just being told to use a formula. Last month, Shunya asked this kind of question, which gave me a chance to refer to our archive and go beyond it.
Arrhenius Equation: Which Graph is Right?
(New Question of the Week) Occasionally we get questions challenging the correctness of a textbook problem, or of a test grade. And sometimes we get questions about mathematics used in sciences like physics or chemistry, which lead us to explore unfamiliar fields. The most interesting question this week is one of these. It is one …
When Do I Add or Multiply in Probability?
Probability is a subject in which it can be quite difficult to see at a glance what method to use. There are many ways in which its ideas can be combined. Two principal ways are “or” and “and”: What is the probability that I draw an ace or a spade? How about an ace and …
How Can I Remember Area Formulas?
Students often ask about formulas for areas or volumes. Sometimes they are just overwhelmed by the number of formulas they need to know; other times they are curious about how we know they are true. The answer to both questions is, in part, the same: if you know at least something of where they come …