Quit Paradoxes Schrödinger’s Cat Coastline of Ireland Koch Snowflake.

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Presentation transcript:

Quit

Paradoxes Schrödinger’s Cat Coastline of Ireland Koch Snowflake

QuitParadoxes Mathematics cannot be applied to everything, and cannot explain everything. A paradox is a set of statements which contain contradictions. The existence of paradoxes causes problems for mathematical logicians which they cannot solve.

Quit 20 people live on an island. Some people cut their own hair, the rest use the barber who only cuts the hair of people who do not cut their own hair. 10 people never cut their own hair. Draw a Venn diagram of the people on the island: Russell’s Paradox

Quit Let A = people who cut their own hair Let B = people who do not cut their own hair Russell’s Paradox AB In which circle is the barber?

Quit A cat is placed inside a box, a device which operates randomly is placed inside the box which will release a deadly gas killing the cat. There is no way of knowing without opening the box if the cat is alive or dead. Logically the cat is either alive or dead, so we simply open the box to find out which! Schrödinger’s Cat

Quit Schrödinger’s Cat

Quit Coastline of Ireland How long is the coastline of Ireland? If we use a 10 km stick to measure it, we might get 2,500 km. As we measure it in more and more detail going in and around every cove it will grow to 25,000 km. If we look close enough we can make it 100,000 km or any length we wish!

Quit Coastline of Ireland

Quit Koch Snowflake Helge von Koch (1870 – 1924) Draw a simple equilateral triangle On each of the three sides place another equilateral triangle exactly one third and in the middle of the side Continue with each of the new sides

Quit Koch Snowflake

Quit Koch Snowflake

Quit Koch Snowflake

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