Can you solve it? Here’s (not) looking at Euclid | Mathematics

The ancient Greek Greek Euclid presented a list of five axioms that he held to be clearly correct. They (or equalize):

1. You can draw a line between any two points.

2. You can extend the lines indefinitely.

3. You can draw a circle at any time with any radius.

4. All correct angles are equal.

5. All triangles have internal corners that add up to 180 degrees.

Euclidean engineering is what we learn in school, and only applies to flat surfaces. The inner corners of the triangle on a curved surface no Add up to 180 degrees – the subject of puzzles today.

1. Correct, correct, correct.

Suppose the Earth is a perfect ball. Imagine drawing a straight line from the Arctic to a point on the equator. Can you draw two identical lines to create a triangle where all internal angles are correct angles (that is, they add up to 270 degrees in general)?

2. Complete circle

After that, let’s go larger, angle. Can you find a way to cover the Earth with equal triangles that have internal corners of up to 120 degrees (that is, it adds up to 360 degrees in general)? These triangles should be the same size and there should be no overlapping or gaps between them.

(Hint: Think of drawing triangles side by side.)

3. Delicious triangles

Now imagine Donat instead of a ball. Can you draw two identical triangles of the right angle on the cakes so that they cover its surface completely? And what will add the sum of the six interior corners of these two triangles?

(The cake is “Torus”, a cylinder that bends and joins a loop, as in the image above.)

I will return at 5 pm in the United Kingdom. Please not spoilers. Instead, discuss your favorite axioms.

Today, Adam Kusheski, a professor of mathematics at the College of Equatorial Medicine and the author of folklore.

In his wonderful new book Proof: the science of uncertainty Adam tells the story of how thinkers in the nineteenth century began to challenge the facts of Euclids clear – and how this math history was. It is a wonderful reading that covers many areas, including date, politics, statistics, computer science and epidemic, which is the field of Adam’s professional experience.

Evidence Wasse books.

I have prepared a mystery here on Mondays since 2015. I have always been aware of the wonderful puzzles. If you want one suggestion, Send me.