Number is the most important concept in mathematics. Nothing else is as important because MATHEMATICS IS THE ABSTRACT SCIENCE OF MEASURE AND NUMBER. Nothing else! Set theory, topology and group theory are NOT mathematics. Download the best book ever written on the number concept: https://www.academia.edu/105399167/The_Ultimate_Book_of_Numbers Link to presentation: https://www.academia.edu/116556934/How_to_teach_number_concept_to_teenagers In my free eBook above, I also show you how to teach your toddler all the four basic operations! You would not know how to do even the most basic fraction arithmetic had my Ancestors had the same shit-for-brains as contemporary mathematics academics: https://www.academia.edu/69488136/Theory_of_fractions_from_Book_5_of_Elements_for_Dummies Learn about the Holy Grail of Calculus: https://www.academia.edu/105576431/The_Holy_Grail_of_Calculus Get the true Origins and History of Calculus: https://www.academia.edu/106488069/The_Non_fictional_Origins_and_History_of_Calculus Discover closed -form trigonometric functions never realised before: https://www.academia.edu/109334669/Ancient_Greek_trigonometric_formulas_better_than_anything_ever_known Follow me on Academia.edu: https://independent.academia.edu/JohnGabriel30 Donate here: https://gofund.me/af8a5312 or here: https://wise.com/pay/me/johng3933 All my YouTube videos are backed up here: https://odysee.com/@NewCalculus:1 The scum of YouTube are constantly threatening and looking for excuses to shut down my channel. Want to get instant updates for the newest math around? Join our discord server! https://discord.gg/CJ9Ks3WerR Merchandise Store: https://new-calculus.printify.me/products ... https://www.youtube.com/watch?v=WZXHe-swBO0

This is the first of three videos on arithmetic with magnitudes in geometry. There are two main ways of representing ratios. 1. As line segments (magnitudes of any kind will do) separated by a colon 2. As sides of a triangle (proportional ratios are found from similar triangles) A ratio is literally nothing more than a comparison of two magnitudes. For example, if we write ____ : _________ , this means we are comparing the line lengths that appear on either side of the colon. The comparison is a means of identifying the line that appears BEFORE the colon (called the antecedent) using the line that appears AFTER the colon (called the consequent). This is purely a matter of convention. The antecedent and consequent are called aliquot parts of the ratio. We cannot talk about the properties or anything else with respect to ____, unless we have something to compare it against. Euclid defined ratio as follows (Book V, Def.3): Λόγος ἐστὶ δύο μεγεθῶν ὁμογενῶν ἡ κατὰ πηλικότητά ποια σχέσις. Thomas Heath translated it incorrectly as: A ratio is a certain type of condition with respect to size of two magnitudes of the same kind. Heath's translation is just a bunch of baloney. Heath did not understand what was being said which is not surprising because like most mainstream math academics, Heath had no clue what the number concept meant. Here is the correct translation: A ratio is about the quotientness (πηλικότητά) of two homogenous magnitudes. There is no English equivalent for the Greek word πηλικότητά, so I made up the word "quotientness". Euclid writes "ποια σχέσις" meaning "what relationship" or "quotientness". This means that given any ratio, the most important aspect is whether or not the antecedent and consequent parts (called aliquot parts) have a common measure or divisor. Aliquot means part of another whole. This property of having a common measure is called quotientness. There are two possibilities - either the aliquot parts have a common measure or they do not. Can you think of examples? 1:2 has the property of quotientness. circumference : diameter does NOT have the property of quotientness. In geometry it does not matter if the ratios have quotientness or not, because every ratio has the property of proportion with innumerably many other proportional ratios. Using the scheme described above, we can find any proportional ratio using a parallel line which adjusts the aliquot parts as it moves between the vertical and horizontal lines. The concept of measure arises once we choose a "unit" ratio, that is, any ratio whose aliquot parts are equal and assumed as the basis of identifying the antecedent of any other ratio. Since any such ratio ... https://www.youtube.com/watch?v=sznfB7A8fEc