Introduction
Have you ever heard the saying, “what gets bigger the more you take away?” It may seem counterintuitive at first, but in fact, this concept can be found in various areas of math and art. In this article, we will explore the surprising ways in which subtracting, removing, or simplifying elements can actually create more size, complexity, and beauty.
The Surprising Property of Negative Numbers: Why You Gain Size by Subtracting
Let’s start with a basic example: negative numbers. When we subtract a negative number, the result is a positive number. For instance, if we subtract -3 from 5, we get 8. This may seem like a small quirk of mathematics, but it actually has some important implications.
Negative numbers are not just abstract concepts in math; they come up in real life situations all the time. For instance, if you owe someone 5 dollars, you have negative 5 dollars in your bank account. Similarly, temperatures below zero are expressed as negative numbers. When we subtract negative temperatures (e.g. subtracting -5 degrees from -2 degrees), we are actually adding those temperatures together, and the result is a temperature that’s farther from zero, or “bigger” in a sense.
But what about subtracting negative numbers? This is where things get really interesting. When we subtract a negative number, we are actually adding a positive number to the original quantity. For instance, if we subtract -3 from 10, we are adding 3 to 10, resulting in 13. This means that subtracting a negative number can actually make something bigger!
Uncover the Mystery of Mathematics: Discovering How ‘Less’ Can Mean ‘More’
The idea that “less” can actually mean “more” may seem like a paradox, but it’s a key concept in mathematics. Often, decreasing the size of something can actually lead to a bigger overall result. This is especially evident in calculus, where we often use the concept of limits to find the behavior of functions as they approach certain values.
For instance, imagine you want to calculate the area under a curve. You might start by dividing the area into many small, thin rectangles. As you decrease the width of each rectangle, you approach the true area of the curve more accurately. In other words, by making each individual rectangle smaller, you end up with a larger overall area under the curve.
This same concept of smaller pieces creating larger wholes can be found in many other fields, from music (where small notes combine to form melodies) to architecture (where small parts of a building combine to form a grand structure).
The Fascinating World of Recursive Patterns: Exploring How Removing Shapes Creates Bigger Ones
Another important concept in the world of “taking away” is recursion. This is an idea found in math, computer science, and many other fields. Recursion refers to the use of a rule or formula to generate patterns that repeat at smaller and smaller scales.
One example of this is the Sierpinski triangle, which starts with a single equilateral triangle, and then repeatedly removes smaller triangles from its center.
The Sierpinski triangle is an example of a recursive pattern in math and art.
The fascinating thing about recursive patterns is that by removing shapes or sections of them, we can actually reveal new patterns at larger scales. In other words, by taking away certain parts, we can actually create more complexity. This principle is also used in the construction of fractals.
Discovering the Power of Fractals: How ‘Taking Away’ Can Create Stunningly Complex Structures
Fractals are complex geometric shapes that repeat at smaller and smaller scales. They are found in nature (such as the branching patterns of trees or the irregular shapes of mountains) as well as in art and design.
One way fractals are created is by “taking away” or simplifying parts of a design in an iterated process. For instance, the Mandelbrot set is a famous fractal created by iteratively calculating the behavior of a simple equation. Similarly, the Koch snowflake is a fractal created by iteratively removing triangles from an equilateral triangle.
The Mandelbrot set is a famous fractal created by iteratively calculating a simple equation.
What’s interesting about fractals is that they can create stunningly complex structures from simple rules. By iteratively “taking away” parts of a design, we can create intricate, self-similar patterns that are both recursive and scalable. This makes fractals useful in fields like architecture, graphic design, and even video game design.
From Art to Algebra: Understanding How Negative Space Can Create the Illusion of Size and Depth
Finally, let’s turn to the world of art and design, where the idea of “taking away” is often used to create balance, harmony, and contrast. One important concept in this realm is negative space, which refers to the space around an object rather than the object itself.
Negative space can be used to create the illusion of size and depth in a design. By emphasizing the positive space around it, negative space can draw the eye and create a sense of balance. Negative space can also be used to create contrast or emphasis, as in typography or logo design.
For instance, the FedEx logo uses negative space to create an arrow shape between the letters “e” and “x”, emphasizing the company’s focus on precision and speed.
The FedEx logo is an example of how negative space can be used to create contrast and emphasis in design.
Ultimately, the concept of “taking away” can be found in many areas of mathematics and art. Whether it’s through negative numbers, recursive patterns, fractals, or negative space, removing elements can often reveal new patterns and create more size, complexity, and beauty.
Conclusion
In this article, we’ve explored the counterintuitive concept of “what gets bigger the more you take away”. We’ve seen how taking away negative numbers can actually make something bigger, how decreasing the size of something can lead to a larger result, and how recursive patterns and fractals are generated by removing parts of a design. We’ve also seen how negative space can create the illusion of size and depth in a design.
The common thread here is that “taking away” can often create more, whether it’s in math, art, or design. By understanding these concepts, we can not only gain a deeper appreciation for the world around us, but also think more creatively and solve problems more effectively in a variety of fields.
