Unsolved problems – and the search for solutions
‘You have given yourself the trouble to go into matters thoroughly, I see. That is one of the secrets of success in life.’
Anthony Powell, The Kindly Ones, 2nd Movement in A Dance to the Music of Time University of Chicago Press, 1995
“a2 + b2 = c2” is the formula for…?
1. Recipe for Apple Banana Cobbler.
2. Square on the Hypotenuse.
3. Haven’t got a clue.
Answer: a squared + b squared = c squared is the formula for the Square on the Hypotenuse, also known as the Pythagorean Theorem.
the historic Book of Calculation
Puzzles and riddles
made arithmetic available to the masses.
When I studied Geometry and Algebra in high school, I couldn’t quite figure out why we were adding, subtracting and multiplying the letters of the alphabet. In order to understand alphanumeric equations and formulae, I needed to know what these abstractions stood for, and something about their practical use in the real world. Why would I want to know, for instance, the sum of the Square on the Hypotenuse? Let’s say, I am an architect or carpenter and I want to lay out concrete footing for a new building?
The HiStory of Math
When Ancient Egyptians needed a way to lay out square corners for their fields, they surveyed the land by using lengths of rope knotted into 12 equal sections and stretched the rope around three stakes arranged in a triangle. Because they knew that if two sides of a right triangle are known (a and b) you can substitute these values in a formula to find the missing side (c). In a right triangle the square on the hypotenuse equals the sum of the squares of the other two sides. Pythagoreans knew, as did the Egyptians before them, that this formula for the square on the hypotenuse was the “most accurate method available” for making square 90 degree angles.
Pythagorean Theorem Origins
Pythagoras, a Greek philosopher and mathematician born around 530 B.C., is credited with formulating the Pythagorean Theorem. However, it was certainly known earlier. He founded a brotherhood called the Pythagoreans in Crotona, Italy, among the aristocrats of that city, which later came under siege in a political uprising. Pythagoras’ fate is unknown (Sacred Texts).
There is evidence of mathematics coming from China, Egypt, India, Mesopotamia – even from pre-Columbus Mayans in Central America. A number of documents have survived that allow us insight into the ancient Egyptians’ approach to mathematics. The Rhind papyrus reveals the ancient Egyptians were dealing with numbers around 1550 BC. It contains 84 different calculations. A History of the World in 100 objects, by Neil MacGregor.
Although we usually credit the ancient Greeks with laying the groundwork for medicine, other sciences, philosophy and mathematics, the ancient Greeks credited the Kemites (Egyptians). Discovery Channel
Pythagoras, Hippocrates, Socrates, Plato and other Classical Greek thinkers traveled to Kemet to expand their knowledge.
- Hippocrates, who is commonly referred to as “the father of medicine,” studied the Egyptian Imhotep’s method of diagnosis in Kemet. [He] lived 2,500 years before Hippocrates.
- Pythagoras, commonly referred to as “the father of mathematics,” traveled to Kemet where he studied geometry and other mathematics with the Kemetic priests.
Imhotep, Physician, High Priest and Scribe, was chief architect to the Egyptian pharaoh Djoser (reigned c.2630 – c.2611 BC). He was responsible for the world’s first known monumental stone building, the Step Pyramid at Sakkara and is the first architect we know by name.
Aristotle wrote, “Egypt was the cradle of mathematics.” Egypt, of course, was Kemet. Discovery Channel
The Man of Numbers: Fibonacci’s Arithmetic Revolution (Keith Devlin). Until the 13th century, even simple arithmetic was accessible almost exclusively to scholars. Merchants kept track of quantifiables using Roman numerals, performing calculations either by an elaborate yet widespread fingers procedure or with a clumsy mechanical abacus. But in 1202, a young Italian man named Leonardo da Pisa — known today as Fibonacci — changed everything when he wrote Liber Abbaci, a historic book on arithmetic, Latin for Book of Calculation.
Fibonacci “revolutionized everything from education to economics,” using puzzles and riddles to “alleviate the tedium of calculation and making arithmetic available to the masses.”
For Math Geeks and Wizzes
The Story of Maths – Episode 4 To Infinity and Beyond
BBC Documentary (YouTube)
Unsolved problems – and the search for solutions
The Story of Maths
To Infinity and Beyond Short course on OpenLearn
Marcus du Sautoy examines unsolved problems that confronted 20th-century mathematicians.
There are 293 ways to make change for a dollar. Real World Math Lesson Plan (Teachnet)
The story of 1729 and other weird math facts – When Srinivasa Ramanujan, the great Indian mathematician, was ill with tuberculosis in a London hospital, his colleague G. H. Hardy went to visit him. Hardy, trying to initiate conversation, said to Ramanujan, “I came here in taxi-cab number 1729. That number seems dull to me which I hope isn’t a bad omen.”
“Nonsense,” replied Ramanujan. “The number isn’t dull at all. It’s quite interesting. It’s the smallest number that can be expressed as the sum of two cubes in two different ways.” (Ramanujan recognized that 1729 = 13 + 123 as well as 93 + 103.)
Invention of Zero
- The Origin of Zero by John Matson. Much ado about nothing: First a placeholder and then a full-fledged number, zero had many inventors.
Once upon a time there was no zero. Of course people knew if they had nothing, but there was no mathematical notation for it.
- A BRIEF HISTORY OF ZERO by Kristen McQuillin
Let’s not forget the women
Hypatia was an Alexandrine Neoplatonist philosopher in Egypt who was the first well-documented woman in mathematics.
Bottom line, math problems, riddles and puzzles can help sharpen your problem-solving, critical thinking and decision-making skills. If you need to brush-up, try these math refreshers. Feel free to suggest your favorite games and teasers.
For the clueless pdf downloads
- Euclid’s Elements (mathematicalmusingsblog.wordpress.com)
- The Gou Gu Xian Theorem (worldhistory1isobe.wordpress.com)
- International Transmission of Knowledge and Culture