“Horology is quite literally the “study of time”, most often referred to as the art or science of time measurement.” (A World of Time, 2017)

Various methods and instruments were used to record time before the invention of the mechanical clock;

Sundials: Sundials are the oldest known method of telling time, dating back to 3500BC. The sundial relies on the rotation and movement of the sun. The shadows formed by the sun moving from east to west determine the time of the day. The time was measured based on the length of the shadow created. However, there was a downside to this method of time keeping. As the dial relied on the sunlight, this instrument would be useless if it was a cloudy day or if the sun was down. After discovering this issue, new methods of time keeping were developed that were far more reliable. (Marie, 2017)

Egyptian water clocks: The oldest known water clock dates back to 1500 BC. There are two versions of the water clock, outflow and inflow. The outflow clock was where a container (with markings down the side) was loaded with water, enabling the water to drip out an even pace. Individuals were able to tell the time by calculating the amount of water that had leaked from the container. The inflow clock followed the same method as the outflow clock, except instead of using one container, two containers were used. The water from the first container would drip into the second container at a steady pace. Observers were able to tell the time by the amount of water that had leaked from one container to the other. (Ancient Origins, 2014)

Sundials and Egyptian water clocks are just a few of many examples of time keeping. Others include, candle clocks, Astronomical clocks, incense clock are just a few methods that were used before the mechanical clock was created.

Dave Allen gives us an insight into the difficulties (and frustrations) of teaching children the analogue clock.

http://https://www.youtube.com/watch?v=0QVPUIRGthI

This video made me think of the importance of teaching children time. I think it is necessary that children recognise how far the various methods of telling time have developed over the years, as it will provide them with a better understanding of what time really is and will convey to the pupils how we came to using the analogue/digital clock. However, there has been speculation whether it is required for children to learn the analogue clock in our very digital world. I think, yes. Analogue clocks are everywhere, from the clock on our walls to famous landmarks, children need to be able to understand and interpret the time on the analogue clock. Furthermore, analog clocks help children understand the passage of time because they have hands that are consistently moving. Despite living in a high-tech 21^st century, I don’t think it’s time to ditch the analogue clocks just yet.

 

Aworldoftime.co.uk. (2017). What is Horology – A WORLD OF TIME – HOROLOGIST. [online] Available at: http://www.aworldoftime.co.uk/what-is-horology—a-world-of-time—horologist.html [Accessed 27 Nov. 2017].

Ancient Origins. (2014). The Ancient Invention of the Water Clock. [online] Available at: http://www.ancient-origins.net/ancient-technology/ancient-invention-water-clock-001818 [Accessed 27 Nov. 2017].

Marie, N. (2017). When Time Began: The History and Science of Sundials. [online] Timecenter.com. Available at: https://www.timecenter.com/articles/when-time-began-the-history-and-science-of-sundials/ [Accessed 27 Nov. 2017].

Prior to our input with Richard, I was (yet again) confused to how sports and mathematics were linked. I was a keen netball player and coach when I was in school and my main aim when playing would be trying to win the match with my team by using various tactics; not by using mathematics to help achieve this. However, after our input I was eager to find out how maths and netball were connected.

Netball and Mathematics

• The court – the size of the court is 30.5 metres long and 15.25 metres wide and is divided into thirds. The centre circle has a diameter of 0.9 meters and the two shooting semi circles are me
  

  Dsr.wa.gov.au. (2017). Netball. [online] Available at: https://www.dsr.wa.gov.au/support-and-advice/facility-management/developing-facilities/dimensions-guide/sport-specific-dimensions/netball [Accessed 9 Nov. 2017].

  asured at 4.9 metres.
• Positioning – When a player attempts to defend or intercept the ball, they must be at least 0.9 meters away from the player with the ball.
• Speed and accuracy of the pass is key for moving forward and into the shooting semi-circles. The quicker and more accurate the pass is, the less likely the opponent team can intercept it.
• Shooting – A technique that many GS and GA use when shooting is positioning your elbow at a right angle when holding the ball, which improves stability.
• The timings – A netball match lasts an hour and is split into fifteen minute quarters.

Angles, distance, time and speed are just a few of the basic concepts used in mathematics which links to what Liping Ma refers to (Ma, 2010).

http://https://www.youtube.com/watch?v=4w_3D47MEgI

This short video highlights how mathematics is used in sports as a whole. For example, discussing a players statistics which enables them to determine their strengths and weaknesses, deciding where a player is going to be positioned in the game/pitch or even the way in which the game is scored – mathematics is always involved. The clip then goes onto explore how mathematics plays a key role in cricket. Mathematics is used to calculate the total number of overs in a match (an over is a set of six balls bowled from one end of a cricket pitch) and calculate the average and strike of the batsmen and bowlers. The video also suggests that the measurement of the bat and ball can affect the player’s performance within a game. This is further supported by ‘The Physics of Cricket’ as they explain why lighter bats can be swung faster than heavier bats:

“Imagine hypothetically that the bat weighs 10 grams. If you swing it as fast as possible, you might get the tip to travel at 160km/hr. Now double the weight to 20 gm. This time the tip travels at about 159 km/hr. The problem here is that your arms weigh about 8kg all up, so the extra 0.01 kg is hardly noticeable. Most of the effort needed to swing a bat goes into the swinging the arms.” (Physics of Cricket, 2005).

Reflecting on this input, I have discovered that many fundamental concepts are used throughout sport; not only are these concepts reflected in the equipment used in a game e.g. a bat and ball, but are also used by sports players to improve their performance within a game.

Through my journey in discovering mathematics, it has become apparent to me that mathematics is everywhere. The idea of maths being all around us needs to be reflected in the classroom to minimise the idea that maths is not just about equations and fractions; but is in actual fact heavily reflected in our day to day lives e.g. in our favourite sports. Demonstrating how maths can link to pupils interests, makes the subject more enjoyable and relevant (The Scottish Government, 2008).

 

Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.) New York: Routledge.

Physics of Cricket (2005) Available at: http://www.physics.usyd.edu.au/~cross/cricket.html (Accessed: 9 November 2017).

The Scottish Government (2008) curriculum for excellence building the curriculum 3 a framework for learning and teaching. Available at:  http://www.gov.scot/resource/doc/226155/0061245.pdf (Accessed: 9 November 2017).

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface.”                                                                                                               Du Sautoy 2011

Prior to starting the discovering mathematics module, maths and music are very different subjects. I see mathematics as an academic subject whereas music is more creative; which highlights how closed-minded I was.

We were asked at the beginning of the input to think as many links that we could think of between music and maths. After struggling for a few minutes, I think in all we managed to come up with 3 links. We were then shown the list of connections and the list was endless –

• Note values/rhythms
• Beats in a bar
• Tuning/Pitch
• Chords
• Counting songs
• Fingering on music
• Time signature
• Figured bass
• Scales
• Musical Intervals
• Fibonacci sequence

http://https://www.youtube.com/watch?v=zAxT0mRGuoY

This video explores how the famous composer Beethoven was able to create spectacular pieces of music despite spending most of his career being deaf. Beethoven discovered that he was able to see the patterns in the music, therefore was able to know what the music was going to sound like. The clip also explores how our ears are able to detect whether a piece of music is nice sounding (consonance) or not (dissonant) – and how maths is used to determine this.

http://https://www.youtube.com/watch?v=1Hqm0dYKUx4

Wave lengths also provide us with the answer to why it is impossible to tune a piano. The video explains that a when the string of the vibrates, it can only vibrate in certain waves (sin waves) due to the strings being fixed to the end of the instrument. The more bumps in the wave, the higher the pitch and the faster the string has to vibrate. The reason why it is impossible to tune a piano is due to the fact that the instrument has too many strings. The video then goes onto explain in depth why having too many strings is an issue and how they use mathematical equations to solve why it is impossible to tune a piano.

I have found it very fascinating discovering the links between mathematics and music. I will definitely consider combining both subjects together when teaching concepts such as sequence and patterns within my teaching practice.

 

Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available at: https://www.theguardian.com/music/2011/jun/27/music-mathematics-fibonacci (Accessed: 7 November 2017)

“Is God a mathematician? Certainly the universe seems to be reliably understood using mathematics. Nature is mathematics.” (Pickover, 2009)

Throughout this module, there has been a reoccurring theme that maths is everywhere. In our input with Anna, we were introduced to the Italian mathematician Fibonacci. Fibonacci is known for the creation of many sequences, with the golden spiral being his most famous discovery. This particular sequence starts at 0 then 1 then you add the two numbers before you get the next number in the sequence; 0 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 and so on. Fibonacci discovered that if he used squares with this sequence, it would make the perfect spiral.

Fibonacci’s golden spiral can be seen throughout nature, sunflowers is a clear example of this theory. The spirals of the seed pattern of the sunflower contain Fibonacci’s sequence. But why do the sunflowers abide by Fibonacci’s theory? It has been suggested that the sunflowers can pack the maximum amount of seeds if it follows this particular sequence.

Spiral Galaxies is another example of where Fibonacci’s sequence is apparent. The milky way has several spiralled arms that follow in the Fibonacci sequence. After looking into this, I read about how the spiral galaxies does not fit the theories of astronomers. According to the astronomers, “the radial arms should become curved as the galaxies rotate. Subsequently, after a few rotations, spiral arms should start to wind around a galaxy. But they don’t.” (Planet Dolan, 2017).

Finally, the placement of a flowers petals also follows Fibonacci’s sequence. Examples of this is the lily (3 petals), buttercups (5 petals) and daisy’s which have 34 petals. It is said that the flowers follow the sequence of Fibonacci to maximise their exposure to sunlight, which is obviously beneficial for the flower.

These findings make it apparent that mathematics is purposeful. Whether it maximising sun exposure for a plant, or to maxmise the space within something; mathematics makes it beneficial.

 

Mathsisfun.com. (2017). Fibonacci Sequence. [online] Available at: https://www.mathsisfun.com/numbers/fibonacci-sequence.html [Accessed 3 Nov. 2017].

Pickover, C. A. (2009) The Math Book from Pythagoras to the 57^th Dimension, 250 Milestones in the History of Mathematics. London: Sterling.

Planet Dolan | Obscure Facts About Life. (2017). 15 Beautiful Examples of Mathematics in Nature. [online] Available at: http://www.planetdolan.com/15-beautiful-examples-of-mathematics-in-nature/ [Accessed 3 Nov. 2017].