From Da Vinci to a Constraint Problem

I was going through a copy of Leonardo da Vinci's notebooks, and the following short passage caught my attention. To heat the water for the stove of the Duchess, take four parts of cold water and 3 parts of hot water. "Cold water" and "hot water" are both vague terms. But given that this was... Continue Reading →

Why Only Five Platonic Solids in Our Geo-Bio-Chemical World?

The DNA-surrounding capsid of the cold virus and the atomic arrangement of  a certain allotrope of  boron consists of  20 triangles arranged in a three dimensional shape known as a icosahedron. If you form a three-dimensional structure with 8 triangles, you get an octahedron. An example is the molecular structure of the electrical insulator and... Continue Reading →

When Math-Shortcuts Involved Little or No Technology

There are some great tools available to anyone who wants to do math, regardless of the level involved. And whether it's a calculator, spreadsheet or software package, they don't just cater to time-savers. Many are programmable and therefore thought-provoking. But in the old days of hand-calculations, people did not necessarily surrender to tedium. They often... Continue Reading →

Fun With Shapes and Numbers

In the diagram below, in between two circles, each with a radius of 1 meter, three smaller circles are squeezed in, centred at C1 , C2 and C3. If you imagine it was possible to continue drawing and squeezing in more circles until you had a billion of them, how much space would be left between... Continue Reading →

Income Inequality: causes and mathematics

Whether you're a researcher, programmer, doctor or professional athlete, most of the satisfaction you derive from work probably comes from uncovering some truth, problem-solving, treating the ill and mastering a sport, respectively. Money is not the main motivator as long as there's enough to raise a family.  But here's where things get complicated. If you... Continue Reading →

Origin and Properties of e

This story will not begin with how the irrational side of human nature and money are indeed at the root of much evil. Instead we will look at how a 17th century financially related-insight by Jacob Bernouilli eventually led us to the discovery of the irrational nature and properties of the number e. Imagine the... Continue Reading →

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