# CTK Insights

• ## Pages

30 Apr

### Is a Point a Part of a Line?

TweetIs a point a part of a line? The question touches on the fundations of geometry. To be able to answer it, one should probably first clarify the notions that are involved in the question. According to the present day understanding, the notions of point and line are left undefined in geometry. We just get […]

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 […]

20 Apr

### What Is This Shape?

TweetThis is just to record a small discovery. Here are two views of the same 3d shape. What is the shape? I'll add an answer as a comment in a couple of days.

16 Apr

### 00 - Münchausen's Syndrome

TweetType 00 into wolframalpha to observe an uncharacteristic one-liner, "indeterminate". And it is hard not to agree with such a designation. The function f(x, y) = xy is discontinuous at (0, 0) however the value at the origin is defined. Indeed, x0 = 1, while also 0x = 0, for x > 0. On the […]

12 Apr

### Sqrt(-1) does not exist - A. De Morgan

TweetAugustus De Morgan's On the Study and Difficulties of Mathematics was first published by the Society for Diffusion of Useful Knowledge in 1831. I am in possession of the 2005 Dover edition, which - in my view - is a delightful reading. It is well known that the imaginary numbers had a hard time entering […]

12 Apr

### Perverse logic

TweetThe famous British philosopher, mathematician, and author, the Nobel Prize winner, Bertrand Russell was known for his acrimonious wit and sharp observations. One of his oft-quoted pronouncements - when is taken out of context - is a persistent cause of embarrassment to math educators and mathematicians. ... mathematics may be defined as the subject in […]