Koch Snowflake Fractal: Area and Perimeter Calculation @TomRocksMaths

Tom Rocks Maths | Koch Snowflake Fractal: Area and Perimeter Calculation @TomRocksMaths | Uploaded 4 years ago | Updated 4 hours ago
The Koch Snowflake is one of the simples fractals to construct, but yet displays some very interesting mathematical properties. In this video made for Maths Week London, we calculate the perimeter and area of the fractal leading to some rather surprising results… The perimeter is shown to be infinite, whilst the area remains constant.

The first part of the video on perimeter is designed for Key Stage 4 students (14-16 years old), whilst the second part on area is designed for Key Stage 5 students (16-18 years old) and above. All ages should be able to follow the instructions to construct their own Koch snowflake fractal at home.

Fractals and the Koch Snowflake 0:00
Perimeter calculation 6:00
Area calculation 14:30

Produced by Dr Tom Crawford at the University of Oxford.

With thanks to Maths Week London, Yami89 and Burt Gulash.

For more maths content check out Tom's website tomrocksmaths.com

You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths.

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$Koch Snowflake Fractal: Area and Perimeter Calculation The Koch Snowflake is one of the simples fractals to construct, but yet displays some very interesting mathematical properties. In this video made for Maths Week London, we calculate the perimeter and area of the fractal leading to some rather surprising results… The perimeter is shown to be infinite, whilst the area remains constant. The first part of the video on perimeter is designed for Key Stage 4 students (14-16 years old), whilst the second part on area is designed for Key Stage 5 students (16-18 years old) and above. All ages should be able to follow the instructions to construct their own Koch snowflake fractal at home. Fractals and the Koch Snowflake 0:00 Perimeter calculation 6:00 Area calculation 14:30 Produced by Dr Tom Crawford at the University of Oxford. With thanks to Maths Week London, Yami89 and Burt Gulash. For more maths content check out Toms website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Tom Rocks Maths logo by Nathanial Butt: https://www.instagram.com/nat_von_b/?hl=en Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths$

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$Mandelbulbs: the search for a 3D Mandelbrot Fractal Follow Tom on his journey to Delft in the Netherlands in his quest to find a 3D Mandelbrot Set, otherwise known as a Mandelbulb. We begin with a discussion of the definition of a fractal, with examples from the natural world, as well as generating our very own in the form of the Koch Snowflake - a shape with infinite perimeter, but finite area. We then define the 2D Mandelbrot Set and introduce the concept of the Hausdorff Dimension which can take non-integer values, as exemplified by the Sierpinski Carpet Fractal. After a brief diversion via the Coastline Paradox and Space-filling Curves, we move onto 3D fractals in the form of the Menger Sponge, before finally using the White-Nylander Formula to generate our 3D renderings of the Mandelbrot Set, otherwise known as Mandelbulbs. Produced by Quark Media - Jamie Halliday and Joseph Brooks Shuttleworth https://quarkmedia.xyz/ Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall at the University of Oxford: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Toms website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths Attribution: Paramount Pictures. ANNIHILATION. YouTube Movies. March 25, 2019. https://www.youtube.com/watch?v=fVILCFvoT1U Mandelbulb renderings from https://mb3d.overwhale.com/ Credits: Geek3: https://commons.wikimedia.org/wiki/User:Geek3 Cwgreene Google Maps Desmos StudyWorld WorldAtlas Zbigniew Fiedorowicz Byron Mayfield$

Oxford University Maths Admissions Test 2023 Question 8

$Making Mathematical Art with L-Systems Tom Rocks Maths intern Max Cairney-Leeming explains how to make mathematical art using Lindenmayer Systems... L-systems consist of lists of symbols which represent a drawing function, and a set of rules that are applied to the symbols iteratively. Starting from a simple axiom - often just a straight line - complex systems can be generated which demonstrate fractal-like behaviour. The Heighway Dragon Curve is one such example, as well as realistic plants and trees that are used in animations in films and video games. Produced by Max Cairney-Leeming with assistance from Dr Tom Crawford. Max is a second year student studying Maths and Computer Science at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Toms website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths Thank you to the following for providing images/video clips under a Creative Commons licence: Schmendreck Icecreeper28 Ryoichi Mizuno Confreaks$

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I teach at BOTH Oxford and Cambridge University