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Showing posts from August, 2021

Algebra Through The Ages

Algebra is such a staple in Mathematics today. It is so prevalent that the concept of algebra i.e. representing unknown values as abstract symbols rather than numbers feels so natural. It is one of the simplest and most utilised weapons in a mathematician’s toolkit. In this article, we will explore the roots of algebra and discover the many contributions to its formalisation all over the world. The earliest known usage of algebra is by the Babylonians around 2000 BC. Using tables and clever geometry – a Babylonian mathematical – the Babylonias could solve quadratic equations. Their methods consisted of step-by-step instructions in dealing with equations of certain forms. The Babylonians actually managed to derive the quadratic formula albeit a very informal version without any of the symbols we use today. There is also evidence of algebra from ancient Egyptian texts circa 1650 BC. Texts from that time, such as the Rhind papyrus, showed that the Egyptians could solve linear equations an

The 7 Bridges of Königsberg

Königsberg was a Prussian city (presently Kalingrad, Russia) in the 18 th century. The city had seven bridges connecting four landmasses as shown in the diagram.   According to folklore, the following question was a popular mathematical puzzle at the time: Could one take a walk through the city in such a way that each bridge would be crossed once? Though many had attempted the problem, they could not prove that their answer was indeed correct. Enter Euler. Euler tackled this problem in 1735, proving exactly why his answer was correct and subsequently creating the field of graph theory. Leonhard Euler (1707-1783) was an extremely prolific mathematician. Most people will know of his constant e, from high school mathematics as well as his multitude of other accomplishments. Euler had such a huge mathematical influence that Pierre-Simon Laplace quoted "Lisez Euler, lisez Euler, c'est notre maître à tous." Which some of you French learners/speakers will know roughly translate