Bifalgorithm post

Mathematics wasn't written down in equations. It was written with words and pictures. Take for example the equation x^2 + 26x = 27. Ancient mathematicians would think of the x^2 term like a literal square with sides of length x. And then 26x, well that would be a rectangle with one side length 26 and the other side of length x. And these two areas together x So now I have two 13x rectangles and I can position them so the new shape I create is almost a square. It's just missing this section down here. But I know the dimensions of this section. It's just 13 by 13. So I can complete the square by adding in a 13 by 13 square. Now since I've added 13 squared or 169 to the left hand side of the equation, I also have to add 169 to the right hand side of the equation to maintain the equality. So now I have this larger square with sides of length x plus 13 and it is equal to 196. Now the square root of 196 is 14. So I know that the sides of this square have length 14, which means x is equal to one. Now this is a great visual way to solve a quadratic equation, but it isn't complete. I mean if you look at our original equation, x equals 1 is a solution. But so is negative 27. For thousands of years, mathematicians were oblivious to the negative solutions to their equations. Because they were dealing with things in the real world. Lengths and areas and volumes. I mean, what would it mean to have a square with sides of length negative 27? That just doesn't make any sense. So for those mathematicians, negative numbers didn't exist.

Mathematics wasn't written down in equations. It was written with words and pictures. Take for example the equation x^2 + 26x = 27. Ancient mathematicians woul…