# CTK Insights

• ## Pages

03 Feb

### What happens to the area when the radius of circle is doubled?

TweetAssume you work with the kids who do not yet know the famous formula for the area of a circle of radius . How would you explain to the kids that the area of the circle quadruples when the radius doubles? This is the question raised by Linda Fahlberg-Stojanovska at the mathfuture google group. For […]

18 Apr

### A Representation of Rational Numbers

TweetOne of the most amusing instances of indirect proof - proof by contradiction - is the establishment of the existence of two irrational numbers and such that is rational. Indeed, is irrational. Then if is rational the problem is solved with . Otherwise, it is solved with and because then . Stan Dolan has recently […]

13 Sep

### The shortest path between two points in a plane

Tweet One of the first challenge problems Paul H. Nahin offers in his new book comes from his experience as a freshman at Stanford. This is a nice yarn. When I was a freshman at Stanford I did well enough during the first two terms of calculus to be allowed to transfer into the honors […]

11 Sep

### Physics Minus Mathematics: The Week of Creation

Tweet Author Paul H. Nahin tells in Introduction to his new book how on several occasions the Nobel Prize winner Richard Feynman spoke condescendingly of mathematics. Nahin suggests that "Mathematics is trivial, but I can't do my work without it" may have been a joke and should not be taken too seriously. He may be […]

29 Apr

### Areas on the Graphs of Power Functions

TweetI have recently come across an article by Atara Shriki of the Technion - Israeli Institute of Technology - where she extended an engaging property of the graph of y = x³ introduced by R. Honsberger. At an arbitrary point P on the graph of y = x³ draw the tangent line and mark its […]