The Mysterious World of Numbers Quiz

Answer: Ulam Spiral

The interesting thing about the Ulam Spiral is that all the prime numbers tend to line up on diagonal lines. The number you start with doesn't even have to be 1; it can be as large as you want and the primes will still line up in diagonal clusters. Nobody knows why prime numbers do this. It's odd that something as orderly as this can be graphed on something as chaotic as a spiral.

Answer: radius and angle

Everyone who's taken algebra is familiar with cartesian coordinates (x, y), but polar coordinates are different. The radius is measured as the distance of a point from the origin, while the angle is the number of degrees from the x-axis. Using trigonometric and periodical functions, polar coordinates are able to graph a wide range of symmetrical figures.

Answer: Fourier Transform

The Fourier Transform is arguably the most important function in all of math. It essentially uses calculus to break up a single wave into all its sinusoidal parts. At any given time there are a multitude of electromagnetic signals zooming around us through space. The Fourier Transform allows receivers and antennae to isolate them so they're easier to identify.

Answer: Tesseract

A tesseract can be unfolded into eight cubes in 3D space, similar to the way a cube can be unfolded into 6 squares in 2D space. A hyperplane is a 4D line segment, a glome is a 4D circle, and a pentatope is a 4D triangle.

In the movie a tesseract was built inside the hyperspace of a Black Hole. How's that for warp travel?

Answer: It can be computed using its antiderivative.

An easy way to think about this is to imagine the area under a curve as an infinite sum of rectangular widths between two points on a function. By using the curve's antiderivative, or the derivative of the function that created it, you can find the answer to whatever depends on its rate of change (for example: the acceleration of an object depends on its velocity).

Many other applications in science and engineering can be used with it. It's remarkable that the area under a curve could yield such results.

Answer: The distance to its perpendicular intersections with each side.

When you draw three perpendicular lines from the triangle's edges to that point, they always add up to its height. This even holds true in higher dimensions.

Answer: 30

In tables that list populations, death rates, stock prices, the area of lakes, etc, the number "1" appears first about 30 percent of the time. The number "9" appears least often, at just under 5 percent. Several theories explaining how this happens have been offered, but it still boggles the mind of many people. Benford's Law has been used to detect fraudulent activities in a number of areas, including accounting and elections.

Answer: imaginary numbers

In the 16th century it was hard to believe that imaginary numbers could have any practical use, but key advances in modern physics wouldn't have been possible without them. Signal processing, fluid dynamics, and quantum mechanics depend on them. Many theoretical concepts use them as well, including Einstein's Relativity, Schroedinger's wave equation, and String Theory. Maybe Einstein was onto something when he said, "Imagination is more important than knowledge."

Answer: You get the same result.

This is known as Euler's polyhedron formula. Mysteriously, the result of the equation equals 2 for every single polyhedron (tetrahedron, cube, octahedron, etc). The formula is so powerful that it serves as a cornerstone of topology.

Answer: Fractals

There are many shapes in nature that are similar to fractals. Leaves, coastlines, wind currents, blood vessels, and snowflakes all appear as fractals from a distance. But once you zoom in, disorder emerges. Something known as Chaos Theory (tiny variations that distort orderly systems) is thought to be the culprit behind nature's inability to generate predictable systems.