The triangle that mathematics loves
 |
Description
Book Introduction
The one unforgettable formula, the Pythagorean theorem.
My encounter with triangles began in textbooks, but the story doesn't stop there! A quirky math communicator, captivated by the allure of triangles, sets out to find triangles hidden in the real world.
"Triangles Loved by Mathematics" is a book that delightfully shows how triangles, geometry, trigonometry, and trigonometric functions are used in everyday life and in cutting-edge technology.
The author welcomes a triangle drawn on an ancient papyrus, meets a planetary scientist, and gets a sneak peek at an unpublished paper on the angle of an asteroid impact.
Hear the struggles of an engineer designing a triangular UFO-shaped glass dome, and create a special disc ball at the request of a math enthusiast DJ.
A triangle is the most basic shape that contains the relationship between distance and angle.
What power do distances and angles possess? From distance measurement to roads, architecture, sports, 3D games, space, music, and even cells, let's discover a vast, previously undiscovered world through triangles, like finding hidden pictures.
My encounter with triangles began in textbooks, but the story doesn't stop there! A quirky math communicator, captivated by the allure of triangles, sets out to find triangles hidden in the real world.
"Triangles Loved by Mathematics" is a book that delightfully shows how triangles, geometry, trigonometry, and trigonometric functions are used in everyday life and in cutting-edge technology.
The author welcomes a triangle drawn on an ancient papyrus, meets a planetary scientist, and gets a sneak peek at an unpublished paper on the angle of an asteroid impact.
Hear the struggles of an engineer designing a triangular UFO-shaped glass dome, and create a special disc ball at the request of a math enthusiast DJ.
A triangle is the most basic shape that contains the relationship between distance and angle.
What power do distances and angles possess? From distance measurement to roads, architecture, sports, 3D games, space, music, and even cells, let's discover a vast, previously undiscovered world through triangles, like finding hidden pictures.
- You can preview some of the book's contents.
Preview
index
preface
1. Distance measurement
2 New angles
3 Laws and Order
4 triangle mesh
5 Fill the space without any gaps
Where do the 6 forms come from?
7 The Magic of Trigonometry
8 Where are we?
9 But is it art?
Creating 10 waves
Conclusion
Acknowledgements
Source of pictures and photos
Search
1. Distance measurement
2 New angles
3 Laws and Order
4 triangle mesh
5 Fill the space without any gaps
Where do the 6 forms come from?
7 The Magic of Trigonometry
8 Where are we?
9 But is it art?
Creating 10 waves
Conclusion
Acknowledgements
Source of pictures and photos
Search
Detailed image
Into the book
One of my favorite stories is from a driller who said, “My day begins and ends with geometry.”
“I literally use trigonometry every day,” one machine builder chimed in.
Workers working in the oilfield even went so far as to detail how unexpectedly important mathematical knowledge was to their careers.
“One of the lessons I learned early on is that your math skills, or rather your aptitude for math, determine how far you can go in this industry.” Learning geometry is essential to progressing from a rig operator (who lowers the next section of drill pipe) to a supervisor who oversees the entire operation.
--- p.11~12
Sometimes we want to know exactly what angle we have traveled.
If you have done two laps, you will return to the starting point.
But in the meantime, I stopped by other places too.
Not only physically, but emotionally too.
So, we might want to say that our current position is equal to 0°, but we've rotated 720°.
This point is especially clear in the world of skateboarding.
--- p.62
Students have the concept that “triangles are strong,” but engineers like triangles because they don’t twist.
For example, a rectangle can be twisted to become a parallelogram.
To prevent the rectangle from twisting, you need to reinforce it by adding a diagonal structure.
That's why engineers like to make structures in a triangular shape.
―What my engineer friend said --- p.113~114
In the early 2000s, an architecture firm designing a new high-rise hotel in Barcelona decided to create a UFO-shaped bar on the rooftop.
They envisioned a structure with a concrete dish-shaped base and a glass dome on top, giving the appearance of a UFO landing on top of a building, as if it were something out of a classic science fiction movie.
The structure was more than 100 meters above ground level.
Making the plate shape out of concrete was easy.
As long as you reinforce it with enough steel, you can pour concrete into any shape.
However, making the glass dome was somewhat difficult.
--- p.132
The Hat had one thing that made it popular with both the public and mathematicians: it was surprisingly simple.
Given that this shape remained elusive to the mathematical community for over 50 years, no one could have predicted that aperiodic single-tiles could be so simple.
It was a 13-sided polygon, which had far fewer sides than I expected.
As expected, it has a concave shape, but there are no separated or broken parts or holes.
When I look at that shape, I get the feeling that it is a deformed equilateral triangle.
The research paper announcing the discovery also described it as “extremely ordinary in its simplicity.”
--- p.203
The reason I like Archimedean solids is because they have a bit more flavor and aroma than the Platonic solids, while still maintaining a pleasing symmetry.
Also included are the truncated octahedron, which we've already met before, and the truncated icosahedron, the classic soccer ball shape.
--- p.228~229
The reason why the trigonometric function table was created in the first place was because it was too difficult to directly calculate the values.
The reason why books containing trigonometric tables were published for a long time is because calculating trigonometric functions was not easy even with a computer.
It took a long time for calculators to provide trigonometric functions, and even longer for them to be small enough to fit in your pocket.
--- p.290~291
The Earth has a magnetic field, but it's not neatly arranged, as is often depicted with iron filings lined up around a bar magnet.
Like gravity, the Earth's magnetic field varies depending on the density and composition of the Earth's interior, causing the magnetic lines of force to meander and move erratically.
A compass simply shows you which direction the local magnetic field around you is pointing.
This is usually considered 'good enough' for navigation, but the difference can be noticeable when compared to GPS or accurate maps.
--- p.330~331
Yes, Alberti's discovery can be summarized in one point: the vanishing point.
He realized that if objects visually got smaller as they got farther away, then everything would converge to a singular point.
And I discovered that in painting, everything should be depicted as if it were being sucked inward.
--- p.351
Pick up a cylindrical fruit or vegetable, such as a long zucchini or carrot, and wrap a piece of paper around it.
And instead of cutting straight across to make a circular cross-section, try cutting at an angle.
When you unwrap the paper, a perfect sine wave will appear.
“I literally use trigonometry every day,” one machine builder chimed in.
Workers working in the oilfield even went so far as to detail how unexpectedly important mathematical knowledge was to their careers.
“One of the lessons I learned early on is that your math skills, or rather your aptitude for math, determine how far you can go in this industry.” Learning geometry is essential to progressing from a rig operator (who lowers the next section of drill pipe) to a supervisor who oversees the entire operation.
--- p.11~12
Sometimes we want to know exactly what angle we have traveled.
If you have done two laps, you will return to the starting point.
But in the meantime, I stopped by other places too.
Not only physically, but emotionally too.
So, we might want to say that our current position is equal to 0°, but we've rotated 720°.
This point is especially clear in the world of skateboarding.
--- p.62
Students have the concept that “triangles are strong,” but engineers like triangles because they don’t twist.
For example, a rectangle can be twisted to become a parallelogram.
To prevent the rectangle from twisting, you need to reinforce it by adding a diagonal structure.
That's why engineers like to make structures in a triangular shape.
―What my engineer friend said --- p.113~114
In the early 2000s, an architecture firm designing a new high-rise hotel in Barcelona decided to create a UFO-shaped bar on the rooftop.
They envisioned a structure with a concrete dish-shaped base and a glass dome on top, giving the appearance of a UFO landing on top of a building, as if it were something out of a classic science fiction movie.
The structure was more than 100 meters above ground level.
Making the plate shape out of concrete was easy.
As long as you reinforce it with enough steel, you can pour concrete into any shape.
However, making the glass dome was somewhat difficult.
--- p.132
The Hat had one thing that made it popular with both the public and mathematicians: it was surprisingly simple.
Given that this shape remained elusive to the mathematical community for over 50 years, no one could have predicted that aperiodic single-tiles could be so simple.
It was a 13-sided polygon, which had far fewer sides than I expected.
As expected, it has a concave shape, but there are no separated or broken parts or holes.
When I look at that shape, I get the feeling that it is a deformed equilateral triangle.
The research paper announcing the discovery also described it as “extremely ordinary in its simplicity.”
--- p.203
The reason I like Archimedean solids is because they have a bit more flavor and aroma than the Platonic solids, while still maintaining a pleasing symmetry.
Also included are the truncated octahedron, which we've already met before, and the truncated icosahedron, the classic soccer ball shape.
--- p.228~229
The reason why the trigonometric function table was created in the first place was because it was too difficult to directly calculate the values.
The reason why books containing trigonometric tables were published for a long time is because calculating trigonometric functions was not easy even with a computer.
It took a long time for calculators to provide trigonometric functions, and even longer for them to be small enough to fit in your pocket.
--- p.290~291
The Earth has a magnetic field, but it's not neatly arranged, as is often depicted with iron filings lined up around a bar magnet.
Like gravity, the Earth's magnetic field varies depending on the density and composition of the Earth's interior, causing the magnetic lines of force to meander and move erratically.
A compass simply shows you which direction the local magnetic field around you is pointing.
This is usually considered 'good enough' for navigation, but the difference can be noticeable when compared to GPS or accurate maps.
--- p.330~331
Yes, Alberti's discovery can be summarized in one point: the vanishing point.
He realized that if objects visually got smaller as they got farther away, then everything would converge to a singular point.
And I discovered that in painting, everything should be depicted as if it were being sucked inward.
--- p.351
Pick up a cylindrical fruit or vegetable, such as a long zucchini or carrot, and wrap a piece of paper around it.
And instead of cutting straight across to make a circular cross-section, try cutting at an angle.
When you unwrap the paper, a perfect sine wave will appear.
--- p.382
Publisher's Review
★ New York Times bestseller immediately after publication ★
★ Amazon's Best Books of 2024 ★
“Useful and essential sides of a triangle,
And I will show you all the useless aspects of it.”
The one unforgettable formula, the Pythagorean theorem.
His encounter with triangles began in textbooks, but the story doesn't stop there! Matt Parker, a quirky math communicator who's captivated by triangles, sets out to find triangles hidden in the real world.
"Triangles Loved by Mathematics" is a book that delightfully shows how triangles, geometry, trigonometry, and trigonometric functions are used in everyday life and in cutting-edge technology.
The author welcomes a triangle drawn on an ancient papyrus, meets a planetary scientist, and gets a sneak peek at an unpublished paper on the angle of an asteroid impact.
Hear the struggles of an engineer designing a triangular UFO-shaped glass dome, and create a special disc ball at the request of a math enthusiast DJ.
A triangle is a basic shape that contains the relationship between distance and angle.
What power do distances and angles possess? From distance measurement to roads, architecture, sports, 3D games, space, music, and even cells, let's discover a vast, previously undiscovered world through triangles, like finding hidden pictures.
Where there is science, engineering, and technology, there is a triangle.
The Secret of the Simple, yet Versatile Triangle
“Isn’t math useless?” is a very common question.
One thing is certain: even if you can't predict where and how math will be needed right now, knowing math will be an advantage wherever you go.
In this book, Matt Parker, a popular British math YouTuber who spreads the fun of math, reveals the charm of triangles, which have not received much attention until now.
A triangle is the basic unit representing distance and angle, and is the simplest shape that can create various shapes and mathematical patterns. It is the most practical mathematical tool that creates and supports the real world.
In this book, Parker meets scientists, engineers, and various technologies on his journey to find the triangle.
Let's break away from the triangles and trigonometry we learned in school and discover triangles in the bigger world.
△ In 2022, NASA conducted an experiment to prepare for an asteroid impact with Earth (DART plan).
It was an attempt to see if an asteroid's orbit could be changed by physical impact.
An object with a mass of about 500 kg was sent crashing into the asteroid at a speed of about 6 km per second. Scientists were unable to wait for the results and calculated not only the angle of impact but also the angle of the ejecta that would be ejected from the crater upon impact.
― 2_New angle
△ In the early 2000s, an architectural firm was designing a high-rise hotel in Barcelona and decided to create a UFO-shaped bar covered with triangular glass panels on the roof.
The task of implementing this was assigned to Parker's engineer friend Paul.
Paul found a way to cover the surface of a regular icosahedron, which is made up of 20 equilateral triangles, with numerous triangles, then inflate it like a balloon and use some of the top as a roof.
― 4_Triangle mesh
△ All waves can be expressed as a combination of pure sine waves.
A song is made up of many sine waves, which combine to create a much more complex sound.
It's not easy to break it down the other way around, but it's possible.
Fourier analysis is like the greatest musical interpreter imaginable.
This way you can listen to any sound and break it down into its constituent frequencies.
― 10_Creating waves
A Math Communicator's Intriguing Triangle Exploration
The amazing world of triangles that began with curiosity
△ Can you divide it into three equal parts so that the amount of sandwich and bread crust is the same?
△ How much does the angle change when riding a motorcycle around a race track?
△ If we cover the floor with tiles of a shape other than square, what polygons are possible?
△ How about making a special mathematical mirror ball that hangs from the ceiling at a DJ party?
You can ask questions about objects made of triangles and angles.
In this book, author Matt Parker begins mathematics with curious, out-of-the-box questions.
Following these questions, which may not be of any use but are nevertheless curious, will take you from triangles to geometry, trigonometry, sine waves, waves, and Fourier analysis.
On this journey, you will be able to broaden your mathematical horizons to the worlds of physics, space, biology, and music.
Feeling overwhelmed? If you're simply curious about what else there is to say about triangles beyond the Pythagorean theorem and the sine and cosine functions, you can easily read this book as a math communicator's triangular journey.
Whether you hate math or are familiar with triangles, the author's goal is to show you all the useful, essential, and useless aspects of triangles.
The first aperiodic single tile was discovered in 2023.
A non-periodic single tile is a single tile that fills the plane without any gaps, but in which the same pattern is not repeated at regular intervals.
It was named 'the Hat' because it looked like a hat, and in the UK, it was made known through mainstream media, and the public enjoyed the discovery in various ways, such as 3D printing 'hats' and baking 'hat'-shaped cookies.
Just as science has become more accessible to the general public, let's enjoy mathematics as a form of popular culture.
It's okay if you don't know what it's useful for.
Let's awaken your curiosity about triangles through this book.
A delightful and surprising introduction to the many applications of trigonometry, from the practical to the downright impractical.
― The Financial Times
Although not a textbook, teachers will find many interesting and useful lesson ideas in this book.
― The Wall Street Journal
Parker has a lot of fun with this material and makes it playful.
― The Telegraph
It's rare for a book about mathematics to be so humorous.
Regardless of your math preferences, Parker delivers once again.
― 『Kirkus Review』
It's interesting, funny, and eye-opening.
― 『Book Page』
★ Amazon's Best Books of 2024 ★
“Useful and essential sides of a triangle,
And I will show you all the useless aspects of it.”
The one unforgettable formula, the Pythagorean theorem.
His encounter with triangles began in textbooks, but the story doesn't stop there! Matt Parker, a quirky math communicator who's captivated by triangles, sets out to find triangles hidden in the real world.
"Triangles Loved by Mathematics" is a book that delightfully shows how triangles, geometry, trigonometry, and trigonometric functions are used in everyday life and in cutting-edge technology.
The author welcomes a triangle drawn on an ancient papyrus, meets a planetary scientist, and gets a sneak peek at an unpublished paper on the angle of an asteroid impact.
Hear the struggles of an engineer designing a triangular UFO-shaped glass dome, and create a special disc ball at the request of a math enthusiast DJ.
A triangle is a basic shape that contains the relationship between distance and angle.
What power do distances and angles possess? From distance measurement to roads, architecture, sports, 3D games, space, music, and even cells, let's discover a vast, previously undiscovered world through triangles, like finding hidden pictures.
Where there is science, engineering, and technology, there is a triangle.
The Secret of the Simple, yet Versatile Triangle
“Isn’t math useless?” is a very common question.
One thing is certain: even if you can't predict where and how math will be needed right now, knowing math will be an advantage wherever you go.
In this book, Matt Parker, a popular British math YouTuber who spreads the fun of math, reveals the charm of triangles, which have not received much attention until now.
A triangle is the basic unit representing distance and angle, and is the simplest shape that can create various shapes and mathematical patterns. It is the most practical mathematical tool that creates and supports the real world.
In this book, Parker meets scientists, engineers, and various technologies on his journey to find the triangle.
Let's break away from the triangles and trigonometry we learned in school and discover triangles in the bigger world.
△ In 2022, NASA conducted an experiment to prepare for an asteroid impact with Earth (DART plan).
It was an attempt to see if an asteroid's orbit could be changed by physical impact.
An object with a mass of about 500 kg was sent crashing into the asteroid at a speed of about 6 km per second. Scientists were unable to wait for the results and calculated not only the angle of impact but also the angle of the ejecta that would be ejected from the crater upon impact.
― 2_New angle
△ In the early 2000s, an architectural firm was designing a high-rise hotel in Barcelona and decided to create a UFO-shaped bar covered with triangular glass panels on the roof.
The task of implementing this was assigned to Parker's engineer friend Paul.
Paul found a way to cover the surface of a regular icosahedron, which is made up of 20 equilateral triangles, with numerous triangles, then inflate it like a balloon and use some of the top as a roof.
― 4_Triangle mesh
△ All waves can be expressed as a combination of pure sine waves.
A song is made up of many sine waves, which combine to create a much more complex sound.
It's not easy to break it down the other way around, but it's possible.
Fourier analysis is like the greatest musical interpreter imaginable.
This way you can listen to any sound and break it down into its constituent frequencies.
― 10_Creating waves
A Math Communicator's Intriguing Triangle Exploration
The amazing world of triangles that began with curiosity
△ Can you divide it into three equal parts so that the amount of sandwich and bread crust is the same?
△ How much does the angle change when riding a motorcycle around a race track?
△ If we cover the floor with tiles of a shape other than square, what polygons are possible?
△ How about making a special mathematical mirror ball that hangs from the ceiling at a DJ party?
You can ask questions about objects made of triangles and angles.
In this book, author Matt Parker begins mathematics with curious, out-of-the-box questions.
Following these questions, which may not be of any use but are nevertheless curious, will take you from triangles to geometry, trigonometry, sine waves, waves, and Fourier analysis.
On this journey, you will be able to broaden your mathematical horizons to the worlds of physics, space, biology, and music.
Feeling overwhelmed? If you're simply curious about what else there is to say about triangles beyond the Pythagorean theorem and the sine and cosine functions, you can easily read this book as a math communicator's triangular journey.
Whether you hate math or are familiar with triangles, the author's goal is to show you all the useful, essential, and useless aspects of triangles.
The first aperiodic single tile was discovered in 2023.
A non-periodic single tile is a single tile that fills the plane without any gaps, but in which the same pattern is not repeated at regular intervals.
It was named 'the Hat' because it looked like a hat, and in the UK, it was made known through mainstream media, and the public enjoyed the discovery in various ways, such as 3D printing 'hats' and baking 'hat'-shaped cookies.
Just as science has become more accessible to the general public, let's enjoy mathematics as a form of popular culture.
It's okay if you don't know what it's useful for.
Let's awaken your curiosity about triangles through this book.
A delightful and surprising introduction to the many applications of trigonometry, from the practical to the downright impractical.
― The Financial Times
Although not a textbook, teachers will find many interesting and useful lesson ideas in this book.
― The Wall Street Journal
Parker has a lot of fun with this material and makes it playful.
― The Telegraph
It's rare for a book about mathematics to be so humorous.
Regardless of your math preferences, Parker delivers once again.
― 『Kirkus Review』
It's interesting, funny, and eye-opening.
― 『Book Page』
GOODS SPECIFICS
- Date of issue: September 10, 2025
- Page count, weight, size: 432 pages | 512g | 153*224*21mm
- ISBN13: 9791164053377
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