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Posts Tagged ‘Euclid

“The laws of nature are but the mathematical thoughts of God”*…

 

euclid

2,300 years ago, Euclid of Alexandria sat with a reed pen–a humble, sliced stalk of grass–and wrote down the foundational laws that we’ve come to call geometry. Now his beautiful work is available for the first time as an interactive website.

Euclid’s Elements was first published in 300 B.C. as a compilation of the foundational geometrical proofs established by the ancient Greek. It became the world’s oldest, continuously used mathematical textbook. Then in 1847, mathematician Oliver Byrne rereleased the text with a new, watershed use of graphics. While Euclid’s version had basic sketches, Byrne reimagined the proofs in a modernist, graphic language based upon the three primary colors to keep it all straight. Byrne’s use of color made his book expensive to reproduce and therefore scarce, but Byrne’s edition has been recognized as an important piece of data visualization history all the same…

Explore elemental beauty at “A masterpiece of ancient data viz, reinvented as a gorgeous website.”

* Euclid, Elements

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As we appreciate the angles, we might spare a thought for Kurt Friedrich Gödel; he died on this date in 1978.  A  logician, mathematician, and philosopher, he is considered (along with Aristotle, Alfred Tarski— whose birthday this also is– and Gottlob Frege) to be one of the most important logicians in history.  Gödel had an immense impact upon scientific and philosophical thinking in the 20th century.  He is, perhaps, best remembered for his Incompleteness Theorems, which led to (among other important results) Alan Turing’s insights into computational theory.

Kurt Gödel’s achievement in modern logic is singular and monumental – indeed it is more than a monument, it is a landmark which will remain visible far in space and time. … The subject of logic has certainly completely changed its nature and possibilities with Gödel’s achievement.                  — John von Neumann

kurt_gödel source

 

Written by LW

January 14, 2019 at 1:01 am

Everything goes better with sharks…

 

Sharks!

Given the successes of “Shark Week” and Sharknado, it’s a sure bet that Hollywood will move to remake the classics to feature those creepily-cartilaginous predators.  See what to expect at Sharks Make Movies Better.

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As we decide that it isn’t yet, perhaps, safe to go back into the water, we might might send carefully-calculated birthday greetings to Giovanni Girolamo Saccheri; he was born on this date in 1667.  A Jesuit priest and Scholastic philosopher, Saccheri is probably best remembered for his attempt to disprove the fifth postulate of Euclid (“through any point not on a given line, one and only one line can be drawn that is parallel to the given line”).  In fact, Saccheri’s thinking closely mirrored that of Omar Khayyám’s 11th Century Discussion of Difficulties in Euclid (Risâla fî sharh mâ ashkala min musâdarât Kitâb ‘Uglîdis)– though it’s not clear that Saccheri knew the earlier work.

In any case, Saccheri’s Euclides ab omni naevo vindicatus (Euclid Freed of Every Flaw, 1733) helped lay the foundation for what we now call Non-Euclidean Geometry.

 source

 

Written by LW

September 5, 2013 at 1:01 am

Got your number…

Euler’s Number (e): 2.7182…

Euler’s number is also known as the exponential growth constant. It is the base for natural logarithms and is found in many areas of mathematics.

Application: In finance, Euler’s number is used to determine compound interest, which is extremely vital in understanding the time value of money — the backbone of finance.

Moreover, Euler’s number is crucial when describing any decaying relationship – think Carbon 14 dating.

… and then there are the other 9 “10 Most Important Numbers in the World.”

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As we activate the abaci, we might send carefully-calculated birthday wishes to Stephen Smale; the Wolf Prize-winning mathematician was born on this date in 1930.  Among many other accomplishments, Smale helped develop the logistic model for population growth– one of the foundational insights that allowed the development of chaos theory (and thus, enhanced our understanding of the way in which natural systems actually work)– one of the 17 Equations That Changed the World:

Written by LW

July 15, 2012 at 1:01 am

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