Maths Stuff 2: Alex's Adventures in Numberland (Part 1)
Hello my beautiful friends!
In preparation for my Oxford interview (if I do get an interview), I am slowly re-reading and making notes on the books included in my personal statement. Usually, the maths interviews are focused on your mathematical ability rather than your personal statement, but it is useful to have a good understanding of these books to ensure that you can confidently talk about the topics if necessary. In this post, I am going to summarise the first half of Alex's Adventure's in Numberland by Alex Bellos, so be prepared for a second half. I am going to write about the topics I found the most important and interesting.
Through this book, I discovered that humans instinctively assume numbers are on a logarithmic scale as this is a key survival instinct. Currently, this is shown by tribes such as the Munduruku. Due to this, animals in the wild have better approximation skills than humans whilst humans have a number system instead. Whilst animals do not naturally grasp the cardinality and ordinality of numbers, this can be taught to animals, as demonstrated through the chimpanzee Ai and the research project she has participated in.
Chapter one, succeeding chapter 0, focused on bases. Bases have developed from so-called 'body tally' systems, and thus the most common bases are 5, 10 and 20. Despite base 12 being the scientifically 'easiest' base, base 10 (the base we currently use) is the most suited to human anatomy. Tally systems founded the counting numbers we are currently familiar with. The way these numbers are said, for example 11 = "eleven", can make number systems easier or harder to manipulate.
Being a numerologist is a certain profession whereby you believe numbers express qualities (e.g. personalities, futures) rather than quantities. Pythagoras, it can be argued, was a numerologist because he believed numbers were the "essence of nature". Whilst Pythagoras' name goes to the famous Pythagoras' Theorem, mathematicians such as Bhaskara published similar proofs to Pythagoras before his era. Other mathematics published further proofs after the Pythagorean era, including Leonardo de Vinci.
The topic I found the most interesting in the book so far is about the periodicity and non-periodicity of tessellations. Penrose's discovery of tiles that can only tessellate in a non-periodic way has links to science since it lead to the discovery of the quaicrystal. The art of origami has stretched geometry further and can be used to make many shapes aside from the platonic solids. Further, the Menger Sponge is a shape with an infinite surface area.
Place value has become an integral aspect of our number system and was founded by the Indians. Initially, the West were suspicious of using the magical '0' as a place holder, although it eventually became a much more efficient way of doing calculations. Vedic Mathematics, which was founded in India and provides the foundations of much mathematical theory, consists of 16 alphorisms/sutras from the Vedas providing these foundations.
Bellos then goes on to discuss Pi. Predictions for Pi date back to the biblical era, although Archimedes created the first apparatus for calculating Pi. Following Archimedes' apparatus, other mathematicians found methods of calculating Pi. Leibniz and Zacharias Dase created infinite series for calculating Pi, but, arguably. Dase's series was 'simpler'. Pi is classified as a transcendental number and is used to determine the reliability of computers in the modern day by using computers to calculate Pi to an increasing number of decimal places. Regarding whether Pi is a normal number, these is no proof so far to determine whether Pi is normal or not.
Of course, Pi is used to calculate the circumference of a circle. Circles can be used as wheels and rollers. Equally, the Reuleaux triangle can be used for rollers, but not wheels.
I hope this summary of the first few chapters of Alex's Adventures in Numberland has been useful. Whatever subject you plan on studying at university, I recommend doing wider reading for personal statement purposes and to expand your own interests. Feel free to read my super-curriculars blog post for more super-curricular information. What super-curricular activities do you recommend?
In preparation for my Oxford interview (if I do get an interview), I am slowly re-reading and making notes on the books included in my personal statement. Usually, the maths interviews are focused on your mathematical ability rather than your personal statement, but it is useful to have a good understanding of these books to ensure that you can confidently talk about the topics if necessary. In this post, I am going to summarise the first half of Alex's Adventure's in Numberland by Alex Bellos, so be prepared for a second half. I am going to write about the topics I found the most important and interesting.
Through this book, I discovered that humans instinctively assume numbers are on a logarithmic scale as this is a key survival instinct. Currently, this is shown by tribes such as the Munduruku. Due to this, animals in the wild have better approximation skills than humans whilst humans have a number system instead. Whilst animals do not naturally grasp the cardinality and ordinality of numbers, this can be taught to animals, as demonstrated through the chimpanzee Ai and the research project she has participated in.
Chapter one, succeeding chapter 0, focused on bases. Bases have developed from so-called 'body tally' systems, and thus the most common bases are 5, 10 and 20. Despite base 12 being the scientifically 'easiest' base, base 10 (the base we currently use) is the most suited to human anatomy. Tally systems founded the counting numbers we are currently familiar with. The way these numbers are said, for example 11 = "eleven", can make number systems easier or harder to manipulate.
Being a numerologist is a certain profession whereby you believe numbers express qualities (e.g. personalities, futures) rather than quantities. Pythagoras, it can be argued, was a numerologist because he believed numbers were the "essence of nature". Whilst Pythagoras' name goes to the famous Pythagoras' Theorem, mathematicians such as Bhaskara published similar proofs to Pythagoras before his era. Other mathematics published further proofs after the Pythagorean era, including Leonardo de Vinci.
The topic I found the most interesting in the book so far is about the periodicity and non-periodicity of tessellations. Penrose's discovery of tiles that can only tessellate in a non-periodic way has links to science since it lead to the discovery of the quaicrystal. The art of origami has stretched geometry further and can be used to make many shapes aside from the platonic solids. Further, the Menger Sponge is a shape with an infinite surface area.
Place value has become an integral aspect of our number system and was founded by the Indians. Initially, the West were suspicious of using the magical '0' as a place holder, although it eventually became a much more efficient way of doing calculations. Vedic Mathematics, which was founded in India and provides the foundations of much mathematical theory, consists of 16 alphorisms/sutras from the Vedas providing these foundations.
Bellos then goes on to discuss Pi. Predictions for Pi date back to the biblical era, although Archimedes created the first apparatus for calculating Pi. Following Archimedes' apparatus, other mathematicians found methods of calculating Pi. Leibniz and Zacharias Dase created infinite series for calculating Pi, but, arguably. Dase's series was 'simpler'. Pi is classified as a transcendental number and is used to determine the reliability of computers in the modern day by using computers to calculate Pi to an increasing number of decimal places. Regarding whether Pi is a normal number, these is no proof so far to determine whether Pi is normal or not.
Of course, Pi is used to calculate the circumference of a circle. Circles can be used as wheels and rollers. Equally, the Reuleaux triangle can be used for rollers, but not wheels.
I hope this summary of the first few chapters of Alex's Adventures in Numberland has been useful. Whatever subject you plan on studying at university, I recommend doing wider reading for personal statement purposes and to expand your own interests. Feel free to read my super-curriculars blog post for more super-curricular information. What super-curricular activities do you recommend?
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