Here are some remarks that you may find useful to improve your presentation. So if I want to use a squaring operation to transform my unit square so that its length is -1, I have to multiply it by “i” to rotate it by 90°, and then by “i” again to rotate it by another 90°. In geometric terms, just as multiplying by -1 can be thought of as a reflection, so multiplying by “i” can be thought of as a rotation around the imaginary axis. on the x, y, and z axes, we have “i”, “2i”, “3i” etc. You can find out more about Euler in a video I've produced all about Euler's Identity.Īny number in the imaginary dimension is known as an imaginary number and is given the symbol “i”. It wasn't until the nineteenth century and the work of Leonhard Euler on his famous identity, that the imaginary dimension became more widely accepted. He disliked it so much, that he called it the imaginary dimension, for he too was hard-pressed to believe in its existence. René Descartes, the 17th-century philosopher, and mathematician, who gave us the Cartesian coordinate system, wrote about it in 1637 and was rather derogatory about the idea. However, they were reluctant to believe it. This new dimension is something else entirely.įor centuries, mathematicians suspected that this new dimension might exist. I've only drawn it as such here so that I can represent it on a diagram. However, this third dimension is not the regular third dimension that we're all familiar with from our everyday 3D world. However, once we draw the same diagram in 3 dimensions, we can see it. It rotated into a new dimension which we couldn't see on my two-dimensional diagram. Now we can see where my object went in that first 90° rotation. For example, addition can move the object to the left and subtraction can move it back to the right again. The four mathematical operators can be applied in the world of geometry to perform the four transformations.Īddition and subtraction translate an object. In the same way, as there are four mathematical operators: Addition, Subtraction, Multiplication & Division, there are also four geometric transformations: Translation, Rotation, Scaling & Reflection. Therefore we need a new set of numbers, negative numbers, to represent the idea of money owed.Ĭounting and money are not the only ways we can apply the abstract concept of maths and numbers to the real world. The moment money is involved, we encounter the concept of debt. So this way of teaching them numbers only covers the positive integers.īy the time they reach this age, you might have started giving them pocket money, and all of the sudden, our budding little mathematicians discover that positive numbers are not the only numbers out there. "If I only have two blocks and you want me to give you three blocks. That's all fine and covers everything they need to know about maths, at least while they are young.
"If I have two blocks and you have four, what is the ratio of the number of blocks you have compared to the number of blocks I have?" etc.
"If you have six blocks and you give two of them to me, how many blocks will you have left?" etc.Īs they get older still, we teach them multiplication and division. So we take everyday objects, such as wooden blocks, and ask them to count them.Īs they get older, we teach them addition and subtraction. How do you teach children abstract concepts? You have to apply them to something they can see and touch. But we all learned numbers as young children. Maths in general, and numbers in particular, are very abstract concepts.
Square root of a negative number how to#
Here you will learn what is square root and how to find square root of complex number with examples.Why is “i” the square root of -1? How can there even be a square root of a minus number? Any minus number multiplied by itself gives a positive result, every schoolchild knows that! So how could anything squared ever be negative? To find out, we're going to go back to basics and ask what are numbers?