The above is perhaps the best known formula and is also rarely understood. Although the formula for the area of a circle was already known in Ancient Greece, its justification is not easy at all. So it’s a great topic to enrich the “Why?” series.
⭐️ The area of a circle – formula
As you can see above – a square and a circle of the same area are not “somehow intuitively easy” related. Moreover, it has even been shown that squaring a circle (a procedure performed using a compass and a ruler without a scale) is impossible! And here comes the brilliant idea with a rectangle. Before I tell you what it is, let’s take a look at what the π·r² formula really says.
So there are slightly more than 3 squares of the side r in the circle with radius r.
⭐️ The area of a circle – proof by animation
I worked hard on this animation, I hope you like it. Let me know in the comments 🙂
A small puzzle – the picture presents a mathematical reasoning on the question “What was first – Devil vs Evil?”. Write in the comment an explanation (short) with the answer. The first 10 correct replies will be rewarded with a promotional code enabling the free installation of the Scalar Pro application.
Recently, I was thinking about various justifications for the definition of 0! (factorial of zero) which is
The assumed value of 1 may seem quite obvious if you consider the recursive formula. However, it did not satisfy me “mathematically”. That’s why I decided to write these few sentences. I will give motivations for the less advanced ones, but there will also be motivations for slightly more insiders.
Surely everyone knows that the result of multiplying two negative numbers is positive. The formula “minus times a minus is a plus” or “negative times a negative is a positive” was put into our heads during the early school years. However, the teachers have forgotten to explain why this is the case, and to pass the motivation of mathematicians who defined the arithmetic of negative numbers.
⭐️ Multiplication as a short notation of repeated addition
Functions for mathematics are what elementary particles are for physics. For this reason, the Scalar Calculator and its mathematical engine, provide the syntax for defining user functions, which is as close to natural as possible. Just enter f (x) = x^2 and you are ready to go. Stay tuned to learn a bit more details! 🙂
⭐ Basic user defined functions
The syntax for defining user functions is as follows.
Defining user arguments and constants is what makes Scalar unique in the panorama of available calculators. Take a moment to familiarize yourself with this short tutorial. It is definitely a dose of very useful knowledge. Stay tuned 🙂
After few months of Scalar being present in the Google Play Store, we decided to check what is the distribution of digits (buttons) used by our users directly in the application. Below we present gathered data that say something, but we do not know exactly what. Maybe you will help in the interpretation? Do you see any relation to the Benford’s law?
⭐ Scalar – digits clicks distribution – ordered by digit
The most frequently used numbers are 2 and 5. It is also well visible the effect of multi-use of the digit 0 considering particular user perspective. The digit, that is used the least often, is 7.
When working with Scalar you can enter numbers in the form of fractions and convert decimal numbers into fractions. This is very convenient because fractions function on a par with other numbers, i.e. they are converted to decimal numbers.
⭐ Entering number as fractions
Entering numbers in the form of fractions is done using the following syntax:
Today I will present various types of support for prime numbers that the Scalar calculator provides. There will be some theory, some screenshots, and a few lines of code that you can use directly in your Scalar instances. Stay tuned! 🙂
⭐ Scalar functions and options related to prime numbers
Let’s start with the list of functions and options available in Scalar, which are linked to prime numbers. On the calculator screen, long click on the “example /?” button. As a result you will get the help dialog containing search option. Enter “prime” keyword.
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