Power Tower with @3blue1brown @TomRocksMaths

Tom Rocks Maths | Power Tower with @3blue1brown @TomRocksMaths | Uploaded 4 years ago | Updated 1 hour ago
Grant Sanderson of 3Blue1Brown brings a power tower puzzle to Oxford for us to solve! Featuring self-similarity, convergence versus divergence and cobweb maps, the solution is not quite as straightforward as it first seems...

Find Grant's amazing channel 3Blue1Brown here: youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw

Produced by Dr Tom Crawford at the University of Oxford.

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

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$The Laws of Indices Explained Tom Rocks Maths intern Laura Bradby explains where the laws of indices come from and how negative, zero and fractional powers work. When we first learn about powers, we are usually told that only whole numbers can be used as an index, but this is an over-simplification. By deriving a series of rules or laws for indices, we can in fact calculate zero, negative and fractional powers. The first law states that a^b x a^c = a^(b+c). The second law states that (a^b)^c = a^(bc). Using these laws, we can make a ‘sensible’ definition for zero powers, which must equal 1 for our laws to make sense. This then leads to a definition of negative powers as 1 divided by the positive power. Finally, we derive a rule for fractional powers where the denominator represents a root, and the numerator means to raise the root to that power. Produced by TRM intern Laura Brady – a second year Mathematics student at the University of Oxford – with assistance from Dr Tom Crawford. Tom is an Early-Career Teaching and Outreach Fellow in Mathematics at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-crawford For more maths content check out Toms website https://tomrocksmaths.com/ You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. https://www.facebook.com/tomrocksmaths/ https://twitter.com/tomrocksmaths https://www.instagram.com/tomrocksmaths/ Get your Tom Rocks Maths merchandise here: https://beautifulequations.net/collections/tom-rocks-maths$

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