Mathematics Thread

    Quote

IMAGINARY is a non-profit organisation (German gGmbH) for the communication of modern mathematics. It offers a platform for open and interactive mathematics with a variety of content that can be used in schools, at home, in museums, at exhibitions, or for events and media activities.

Expand  

https://www.imaginary.org/

I think my carpet underlay is made of that stuff

These are two views of the same 3D shape - it's a lattice spanning a 5-, 4-, and 3-fold icosahedron. I generated these images in Processing, writing code to help visualise the geometry for my next origami project.

^love it

    Quote

For more than 20 years, I posed a monthly unsolved recreational mathematics problem, and posted the solutions I received. You can explore the archive of these problems below, by type of problem or by date. I also gathered some of the more interesting unsolved problems here.

Expand  

https://erich-friedman.github.io/mathmagic/index.html

what's your favourite number

  On 2/19/2023 at 3:59 PM, Walter Ostanek said:

what's your favourite number

Expand  

we are obliged to say 70

  On 2/19/2023 at 3:59 PM, Walter Ostanek said:

what's your favourite number

Expand  

twelve

nice little integral

did anyone read the passenger novels by mcCarthy? some fun maths stuff in those - mostly the second one if i remember correctly...obvs I don't understand any of it but sounded cool

    Quote

La La Lab - the Mathematics of Music brings the visitor to an interactive exploration and discovery of music from a mathematical perspective.

Expand  

bohr-mollerup theorem is so badass

https://www.quantamagazine.org/recounting-the-history-of-maths-transcendental-numbers-20230627/

fun vvatch. just mathsy, not math

I really like the idea that the math we use is just some concept we as humans decided to roll with. There are many different options that also make sense and are coherent but we just did not decided to use like these for example: 

Non-Euclidean Geometry
In classical Euclidean geometry, the "parallel postulate" states that given a line and a point not on it, there is exactly one line parallel to the original line that passes through the given point. However, in non-Euclidean geometries like hyperbolic and elliptic geometry, this postulate is replaced, leading to different and equally coherent geometrical systems.

Quaternions and Octonions
In addition to real and complex numbers, there are mathematical systems like quaternions and octonions. Quaternions extend complex numbers by adding two more imaginary components, while octonions add even more. These systems have applications in various fields like computer graphics and string theory.

Modular Arithmetic
In modular arithmetic, numbers "wrap around" upon reaching a certain value, much like a clock. This is different from the arithmetic we learn in school but is crucial in areas like cryptography.

p-adic Numbers
In the p-adic number system, the notion of "closeness" between numbers is different from the one in the real number system. This has applications in number theory.

Fuzzy Logic
In classical logic, a statement is either true or false. Fuzzy logic allows for degrees of truth, which is useful in fields like artificial intelligence and control systems.

Alternative Calculi
The Newtonian and Leibnizian calculus we learn in school is just one approach to understanding rates of change. There are alternative forms like non-standard calculus and constructive calculus.

Tropical Algebra
In tropical algebra, the basic operations are replaced: addition is replaced by taking the minimum, and multiplication is replaced by addition. This has applications in optimization theory and is used to understand things like network flow.

    Quote

How did fighter planes in the 1950s perform calculations before compact digital computers were available? The Bendix Central Air Data Computer (CADC) is an electromechanical analog computer that used gears and cams for its mathematics. It was used in military planes such as the F-101 and the F-111 fighters, and the B-58 bomber to compute airspeed, Mach number, and other "air data".

Expand  

https://www.righto.com/2023/10/bendix-cadc-reverse-engineering.html

  On 10/27/2023 at 7:42 AM, o00o said:

I really like the idea that the math we use is just some concept we as humans decided to roll with. There are many different options that also make sense and are coherent but we just did not decided to use like these for example: 

Non-Euclidean Geometry
In classical Euclidean geometry, the "parallel postulate" states that given a line and a point not on it, there is exactly one line parallel to the original line that passes through the given point. However, in non-Euclidean geometries like hyperbolic and elliptic geometry, this postulate is replaced, leading to different and equally coherent geometrical systems.

Quaternions and Octonions
In addition to real and complex numbers, there are mathematical systems like quaternions and octonions. Quaternions extend complex numbers by adding two more imaginary components, while octonions add even more. These systems have applications in various fields like computer graphics and string theory.

Modular Arithmetic
In modular arithmetic, numbers "wrap around" upon reaching a certain value, much like a clock. This is different from the arithmetic we learn in school but is crucial in areas like cryptography.

p-adic Numbers
In the p-adic number system, the notion of "closeness" between numbers is different from the one in the real number system. This has applications in number theory.

Fuzzy Logic
In classical logic, a statement is either true or false. Fuzzy logic allows for degrees of truth, which is useful in fields like artificial intelligence and control systems.

Alternative Calculi
The Newtonian and Leibnizian calculus we learn in school is just one approach to understanding rates of change. There are alternative forms like non-standard calculus and constructive calculus.

Tropical Algebra
In tropical algebra, the basic operations are replaced: addition is replaced by taking the minimum, and multiplication is replaced by addition. This has applications in optimization theory and is used to understand things like network flow.

Expand  

Ya kinda learn basic modular arithmetics in school before the introduction of rational numbers tho (division with remainder). It's also semi-consciously used in everyday life when reading classic clocks.

A man was pushed from the top of a skyscraper. If the sound of his body hitting the ground reached the killer 5 seconds after the killer pushed him, calculate the height of the skyscraper. The speed of sound in air is 340 m/s, g = 9.81 m/s2. Neglect air resistance.

  On 12/12/2023 at 12:36 PM, Freak of the week said:

A man was pushed from the top of a skyscraper. If the sound of his body hitting the ground reached the killer 5 seconds after the killer pushed him, calculate the height of the skyscraper. The speed of sound in air is 340 m/s, g = 9.81 m/s2. Neglect air resistance.

Expand  

192.781 m?