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Quiz about The Mysterious World of Numbers
Quiz about The Mysterious World of Numbers

The Mysterious World of Numbers Quiz


Math isn't always about number crunching. Step into the rabbit hole and explore some of the stranger areas in the world of numbers.

A multiple-choice quiz by atlas84. Estimated time: 5 mins.
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Author
atlas84
Time
5 mins
Type
Multiple Choice
Quiz #
372,287
Updated
Dec 03 21
# Qns
10
Difficulty
Average
Avg Score
6 / 10
Plays
355
Awards
Top 35% Quiz
Last 3 plays: Guest 75 (8/10), Buddy1 (10/10), pollucci19 (3/10).
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Question 1 of 10
1. A curious pattern emerges when you plot all non-negative numbers in a spiral formation. Circling all the prime numbers on this spiral creates what kind of pattern? Hint


Question 2 of 10
2. Polar coordinates can be used to graph a number of symmetrical objects found in nature, such as hearts, flowers, and leaves. Which two variables are used to graph their images? Hint


Question 3 of 10
3. If you've ever wondered how two radio signals can be heard at the same time, the answer can be found in a function that decomposes a wave-form into its constituent parts. What's this function called? Hint


Question 4 of 10
4. You might know the answer to this if you've seen the movie "Interstellar". What is the name given to a four dimensional cube? Hint


Question 5 of 10
5. What does the Fundamental Theorem of Calculus tell us about the area under a curve between two points? Hint


Question 6 of 10
6. Say you place a random point anywhere inside an equilateral triangle. Viviani's theorem states that the height of the triangle is equal to which three lines that start at the point? Hint


Question 7 of 10
7. In any statistical analysis, Benford's Law can be used to predict how often the number "1" will appear first in a string of numbers. Like the number of Goldberg Variations, what percent of the time does this happen? Hint


Question 8 of 10
8. Bombelli's solution for the square root of negative numbers was rejected by many mathematicians of his time. Chief among them was Descartes, who came up with a disparaging term that we still use today. Now these numbers are used in many advanced mathematical concepts and are essential to describing our world. What are they called? Hint


Question 9 of 10
9. A polyhedron is any three dimensional shape that has multiple faces. With any convex polyhedron, what happens when the number of its edges are subtracted from its vertices and added to its faces (V - E + F)? Hint


Question 10 of 10
10. By iterating a shape or function over and over again, you can find the same patterns emerging on smaller scales inside the main one. The Sierpinski Gasket, Koch Snowflake, and Mandlebrot Set all demonstrate which kind of pattern? Hint



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quiz
Quiz Answer Key and Fun Facts
1. A curious pattern emerges when you plot all non-negative numbers in a spiral formation. Circling all the prime numbers on this spiral creates what kind of pattern?

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.
2. Polar coordinates can be used to graph a number of symmetrical objects found in nature, such as hearts, flowers, and leaves. Which two variables are used to graph their images?

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.
3. If you've ever wondered how two radio signals can be heard at the same time, the answer can be found in a function that decomposes a wave-form into its constituent parts. What's this function called?

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.
4. You might know the answer to this if you've seen the movie "Interstellar". What is the name given to a four dimensional cube?

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?
5. What does the Fundamental Theorem of Calculus tell us about the area under a curve between two points?

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.
6. Say you place a random point anywhere inside an equilateral triangle. Viviani's theorem states that the height of the triangle is equal to which three lines that start at the point?

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.
7. In any statistical analysis, Benford's Law can be used to predict how often the number "1" will appear first in a string of numbers. Like the number of Goldberg Variations, what percent of the time does this happen?

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.
8. Bombelli's solution for the square root of negative numbers was rejected by many mathematicians of his time. Chief among them was Descartes, who came up with a disparaging term that we still use today. Now these numbers are used in many advanced mathematical concepts and are essential to describing our world. What are they called?

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."
9. A polyhedron is any three dimensional shape that has multiple faces. With any convex polyhedron, what happens when the number of its edges are subtracted from its vertices and added to its faces (V - E + F)?

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.
10. By iterating a shape or function over and over again, you can find the same patterns emerging on smaller scales inside the main one. The Sierpinski Gasket, Koch Snowflake, and Mandlebrot Set all demonstrate which kind of pattern?

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.
Source: Author atlas84

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