Required Mathematical Intelligence

Chapter 53 Chaucer's Dilemma

Chaucer himself, who travels with the pilgrims, is a mathematician and a meditator, who is accustomed to go silently, busy thinking about his own problems. "Good friend, I see you often stare at the ground as if you were looking for a rabbit." The innkeeper laughed at him.To his companions' request to narrate history, Chaucer responded with long limericks, distorting the chivalry novels of that era. After 22 lines of verse, the companions declined his recitation and continued to ask for a story.Interestingly, Chaucer poses a little astronomical problem in "The Priest's Prologue," which goes something like this in modern language:
"The sun gets so low from the southern meridian that it's no higher than 29 degrees in elevation as I see it, and I estimate it's about 4 o'clock in the afternoon, because I'm 6 feet tall and the shadow has stretched to about 11 feet .At the same time the height of the moon (which is in Libra) gradually rose, and as we came to the western edge of the country, it all rose." A journalist read it and took the trouble to calculate that the local time was accurate to the minute of 3 58:4, and that day is April 22 or 23 according to the Gregorian calendar.This attests to the precision of Chaucer's account, for the very first line of the Tales mentions that the pilgrimage took place in April, and that they set off on April 4, 1387.

Chaucer figured out this little conundrum and noted it for the interested reader, but he was reluctant to ask his pilgrim friends.What he presented to them was much simpler and could be called a question of geography.

"When in 1372," he said, "I went to Italy as an envoy of our country, His Majesty Edward III, to visit V. Petrarch, the famous poet himself accompanied me on a tour of the top of a mountain. He reminded me, I am astonished that there is less liquid in the cup on the top of the mountain than in the cup at the bottom of the valley. Please tell me why it is possible to have such a strange property on the mountain?"

[Answer: Due to the gravity of the earth, the surface of water or other liquid is always a part of a sphere, and the larger the sphere, the less curvature of its surface, that is, the less convex.On a mountain peak, the surface of any vessel containing a liquid becomes part of a sphere centered at the center of the earth, and the radius of the sphere is larger than that of a vessel placed in a valley. The spherical surface protrudes to a lesser extent from the edge of the vessel.Therefore, the vessel at the peak holds a little less water than the vessel at the bottom. ]
(End of this chapter)