Circle's History and Background
Circles are a such a big part of everyday life and not just in math. The shape of a circle can be found
in food, money, architecture, art, sports, and so much more. Looking back in time the wheel was created
in the 4th millennium BC (10000 years of economy). That was a long time ago. This round object changed the
way of life for people back then. Not only was transportation made easier, but the way of life was simplified.
Things they couldn't imagine doing, they were now able to do. The circle is still doing that today. We are
still experiencing the many ways that circles can make life better. Circles play a crucial role in how we see
the world. It is an amazing tool that helps us to solve problems we wouldn't be able to do without it.
Not only do circles play a big role in mathematics it is also a consistent symbol to a lot of different
contexts. In religions the circle can represent the unity and eternal of something. This is because of
its shape one doesn't know where it stops or where it starts. A circle is used to describe different
paths taken in history or a person metaphorically. Circles can be used in a metaphorical standpoint like
in religion or more concreate in mathematics.
Now, let's dive a little into the etymology behind the word circle
and see what we find. The word
circle comes from, the Latin word circulus, the diminutive form of circus, 'ring, hoop'
(Rubenstein, 2003). When thinking of a circle, ring
and hoop
are great descriptor words,
which makes sense that is what a circle actually means.
Some more interesting etymology about a circle is given by Perisho. The word arc, we use to describe a part
of a circle, came from the game archery. Think about the game of archery. It uses a flat surface usually with
circles on it for the target, and whoever shoots the arrow closer to the center wins. The person uses a bow which
is like half a circle to shoot an arrow at the target. It makes sense where the word arc came from; The word ARC
comes from the Latin arcus (bow, arch, curve)
(Perisho, 1965).
Now another part of a circle is a chord and it comes from the Greek chords' (gut, string of a musical
instrument)
(Perisho, 1965). A string on an instrument is a chord which is just what a chord on a circle
looks like. A chord is a straight-line segment that connects two points on the circumference of a circle.
Understanding the relationship between these words is insightful to understanding the circle.
The last word to look at is circumference. [T]he word arose as a translation of the Greek word meaning outer
surface
or periphery
so means the boundary line of a circle
(Perisho, 1965). The rim of a circle
being called the boundary line of a circle
makes sense. The circumference is just the boundary of the
shape of the circle. Diving into where the names come from helps understand what a circle is more.
However, before going much further let's define what a circle is: circle is a planar shape formed by points
at an equal distance from a fixed point
(Melihan, 2022). It is important that in the definition of a circle
we include that is a planar shape
because otherwise one does not know if a circle or a sphere is
discussed. The other key component is the equal distance from a fixed point.
The equal distance
gives us the nice round shape and the fixed point is usually called either center
or centre
depending on who is writing.
The definition of a circle most used today came from Euclid's postulates. He defined many things in geometry for us.
Ancient Greek geometers were obsessed with constructing things
(Blåsjö, 2022). This is why we have such a good
description and definition of circles. Being able to construct things was very important to them.
Now let's look at the history to why a circle is divided up into $360^\circ$.
According to Bob Sillery, Mesopotamians passed their base-60 numerical system to the ancient
Egyptians, who used it to divide a circle into 360 degrees
(2021). The number 60 was a favorite
of the Mesopotamians because the number was divisible by so many things. It would then only make
sense that then the Egyptians would take the base-60 and have a circle divided into $360^\circ$.
Understanding angles is important. According to Moore, Angle measure and trigonometric functions have been
high school and undergraduate mathematics topics for well over a century
(2013). This shows how important
angles are and when talking about angles usually circles are brought up because the measurement of angles
come from circles.
Circles and angles have an interesting rich background and history. They work together to give us so many things.
Circles have such rich history on how they changed the way people live and still do this in our lives now.