Problem of the Week: 11-08-18: Prove Pasch’s Postulate as a Theorem [Geometry]

Happy 175th birthday Moritz Pasch! The German mathematician was born on November 8, 1843. Pasch specialized in the foundations of geometry. He is best remembered for Pasch's axiom, which he discovered in 1882. 


Although axioms do not require proofs, in this week's problem we celebrate Pasch's birthday by- you guessed it- proving Pasch's axiom. Why? Because proofs are FUN.     


Solution:


Video:

Comments

Post a Comment

Popular posts from this blog

Back to School Math Courses Review Guide

Image
 Oh no, back to school is right around the corner! We know it can be hard to jump straight back into Math classes during the first few days after a summer away. Lucky for you we have arranged some of of our Youtube channel videos into a helpful guide to make sure you are on your game in the first week of class. Check them out below! Trig Functions: If you're starting the year off with any Mathematics class it is a good idea to review the basics of Trigonometric functions. Trigonometry is used in higher level Mathematics classes as well as Physics courses. Unless you dream about the unit circle and trig identities, you are probably like us and have forgotten everything to do with sine, cosine and everything in between. Check out our playlist below. We cover an introduction to radians, inverse trig functions, a quick way to memorize the unit circle and much more! AP Calculus and Calculus I: Both AP Calculus in high school and Calculus I in college focus mostly on differentiation. Ru...
Read more

Some History and Unsolved Problems in Number Theory

Image
Number theory is a very old subject, which is concerned with the set of integers. Number theory started with the concept of integers and simple operations on the integers such as addition, subtraction, etc. Number theory of the greeks is primarily found in the works of Euclid and Plato. Indian mathematicians of antiquity such as Brahmagupta also made significant contributions (one of Brahmagupta's contributions was work on what is now known as Pell's equation). Pierre de Fermat was an important figure in number theory as well, he is responsible for Fermat's theorem as well as Fermat's Last Theorem (a problem which is now solved). Some additional major figures in early number theory were Leonhard Euler, Joseph-Louis Lagrange, and Carl Friedrich Gauss. Eventually number theory itself started to split into recognizable subbranches, two major ones being algebraic number theory and analytical number theory. Analytical number theory is concerned with the use of real and compl...
Read more