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The quote for the day is from Madeleine L'Engel in A Wrinkle in Time. "I don't understand it any more than you do, but one thing I've learned is that you don't have to understand things for them to be."
I recently traveled to France, spent some time in Paris, and had the opportunity to journey to the southern regions of the country. This blog will be a summation of my observations through the tinted lenses of a mathematics cheerleader.
One of the stops touring Paris was the marker, Point Zero. Point Zero is the spot in which all distances from Paris are measured. The distance from Minneapolis, Minnesota to Paris, France is 4203 miles.
Point Zero
The path of a flight from Minneapolis to Paris is an arc that is a portion of a great circle. This arc is called a geodesic.
A great circle is the concept of a line in spherical geometry. Spherical geometry has applications in navigation and astronomy. This type of geometry is termed Non-Euclidean geometry which considers the Euclidean axiom of parallel lines.
Another perspective that I have of point zero is the concept of the origin. The term origin can conjure many meanings. On a Cartesian coordinate system the origin is where the horizontal line (x-axis) and the vertical line (y-axis) meet. This point is designated by the ordered pair (0, 0). Similarly, the Earth has a horizontal line (equator) and vertical line (prime meridian) which intersects in the Gulf of Guinea in the Atlantic Ocean. This point is designated as 0° latitude and 0° longitude.
Prime Meridian Equator
The Mathematical Origin
I also visited the Louvre. The Louvre is massive and impressive but I found a treasure chest of mathematical and scientific wonderments in rooms that displayed items owned by King Louis XIV.
Compasses and Calipers Directional Compasses
Miniature Sundials Globes and Telescopes
Microscopes Scales
Sextants I Have No Clue :-)
The painting, Mona Lisa, created by Leonardo da Vinci hangs in the Louvre and is one of most popular sites. Not only was Da Vinci an artist but he also was a scientist and mathematician. In mathematics, a controversial numeric value is the "Golden Ratio". The Golden Ratio is computed from the following proportion: (a + b)/a = a/b which simplifies to the equation a^2 - ab + b^2 = 0. The solution for this quadratic equation is (1 + sqr(5))/2 or 1.61803398875 (this decimal is an approximation since the golden ratio is an irrational number). This ratio is historically called the ratio of beauty and most famous works of art and architecture supposedly have that particular ratio embedded within them. A "Golden Rectangle" has its ratio of longest side to shortest side as an approximation to that ratio. A "Golden Spiral" is a graph of a logarithmic equation that has the Golden Ratio as its growth factor.
The "Mona Lisa" at the Louvre
The legs of the blue triangle originate in the bottom corners of the painting and bisect the width of the top of the painting. The Golden Rectangle is placed on the left side of the painting with its width progressing across the top of her head. The end of that segment lies on the right side of the triangle. The Golden Spiral frames her face.
When I was in sixth grade, I bought the paperback version of A Wrinkle In Time by Madeleine L'Engel. In fact, I still have it. A quote from the book has stayed with me for a long time. A character in the book, Charles Wallace, explains a tesseract in the following manner, "Well, the fifth dimension's a tesseract. You add that to the other four dimensions and you can travel through space without having to go the long way around. In other words, to put it into Euclid, old-fashioned plane geometry, a straight line is not the shortest distance between two points."
Recently, I watched the movie, Interstellar. In this movie, an astronaut explains the concept of a wormhole. In the explanation, two points are drawn on a piece of paper and a straight line connecting them. The paper is bent so that the two points coincide and a pencil is punched through both holes. That punch represents a wormhole, a portal, which connects one dimension with another.
Towards the end of my stay in France, I had the opportunity to visit an old friend from high school. Jean was an exchange student from France my senior year. We became good friends and previously had seen each other about 20 years ago. There was no rekindling of our friendship, we are still great friends. Our conversations were like we had corresponded consistently for 39 years but in actuality, we hadn't. I have had a few friends in which time has placed a wormhole, in which the tapestry of our lives was folded and 1976 and 2015 became one. The shortest distance between two points is not a straight line.
