Essential mathematical GIFs that will make mathematics finally make sense
Yes, math textbooks are filled with boring, static blocks of text, numbers, and formulas. And nobody, especially students don’t like long tutorials. So, how will students, our future, learn the hardest subject, Mathematics, at school?
In situations like these, I think there is an alternative way to teach Mathematics. It is “the GIFs.” Yes, those funny little video clips that you are always seeing on Twitter. You can ask this;
“How could those goofy moving images be used for education?”
And I can say that fortunately, there are actually so many ways to use GIFs in our classrooms. Although using GIF animations as a technological tool that is very rare in mathematics education, you can do things with these animations that you can’t do with plain text. For instance, instead of telling the students the directions over and over again, just make a GIF for each step. And then the students will see and know it’s important and remember all those parts of a solution or formula. You will keep your students learning and laughing. It could be a cool way to be the coolest teacher at your school.
If you are good so far, let’s take a look at some beautiful mathematical GIFs and learn!
What is π/pi and why is it 3.14something?
Let’s try to measure a circle. The diameter and radius are just straight lines. We can easily measure them with a ruler. But to get the circumference, it is not that easy. The relationship between the circumference of a circle and diameter is so unique. When we divide the circumference by the diameter, we will always get the same number, no matter how big or small the circle gets. But interestingly we can never express it as a ratio of two whole numbers. We can only get close. It is an on-going series of digits starting with 3.14159 and continuing forever! That’s why, instead of trying to write out an infinite number of digits every time, we prefer using the Greek letter π/pi.
Even the students only need the first 2 digits of π, tens of scientists and mathematicians are trying to figure out the mystery of π. They have super power quantum computers and so far they calculated up to two quadrillion digits. And there is a guy who memorized the first 67,000 digits of π.
Question: What happens when we let a circle roll inside a circle that’s exactly twice as big?
Answer: I know, it is too hard to picture in the head. That’s why using a GIF is a perfect way for you.
How many arcs do we need to cover the entire circle?
The length of the arc is r and the circumference is 2πr. It means we would need 2π such arcs to cover the circumference.
Why are the angels in the same segment equal?
For this proof, you can use so many text and geometrical terms, but most of the students will not understand.
If they are not college students, a GIF would work perfectly.
What is the area of a circle?
In the beginning, for high school students, area means “height times base” in general. But when they see they are of the circle which is “π times r²”, they could ask WHY?
How to draw an ellipse? An animation that explains ellipses. The two points marked by small squares are called the “foci” of the ellipse.
There are of 2 ellipses, whose heights are half their widths, adds up to a circle.
What are the first prime numbers and Fibonacci series?
A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number.
Fibonacci Series is a series of numbers in which each number is the sum of the two preceding numbers. The simplest is the series 1, 1, 2, 3, 5, 8, etc.
Mathematics is not just solving for x, it’s also figuring out why.
There are many more applications of Fibonacci numbers. If you look at them closely, you’ll see the Fibonacci numbers buried inside of them. For instance, if you divide the larger number by the smaller number, then these ratios get closer and closer to about 1.618, known to many people as the Golden Ratio, a number which has fascinated mathematicians, scientists, and artists for centuries.
How do we know that a² + b² = c² (Pythagorean Theorem)
Pythagorean theorem, the rule that says for a right triangle, the square of one side plus the square of the other side is equal to the square of the hypotenuse.
In other words, a²+b²=c². This statement is one of the most fundamental rules of geometry.
But how do we know that the theorem is true for every right triangle?
Because we can prove it.
Proofs use existing mathematical rules and logic to demonstrate that a theorem must hold true all the time.
If you’d really like to convince yourself, you could build a turntable with three square boxes of equal depth connected to each other around a right triangle. If you fill the largest square with water and spin the turntable, the water from the large square will perfectly fill the two smaller ones.
How can we draw a triangle with three 90 degree angles on a sphere?
Why do the exterior angles of a polygon equal 360?
How can we construct a square with using circles?
The Haberdasher Problem
For this riddle, with three cuts, we need to dissect an equilateral triangle into a square.
What are the FOIL method and Sum of the First n Natural Numbers?
In elementary algebra, FOIL is a standard method of multiplying two binomials.
- First (“first” terms of each binomial are multiplied together)
- Outer (“outside” terms are multiplied — that is, the first term of the first binomial and the second term of the second)
- Inner (“inside” terms are multiplied — the second term of the first binomial and first term of the second)
- Last (“last” terms of each binomial are multiplied)