Most of geometry is based on two main constructions, circles and straight lines. In geometry, there are many different tools used for construction such as the compass, the straightedge, carpenter’s square, and mirrors. (Princeton) A compass is an instrument that is used to help draw circles. The two most well-known compasses are the modern compass and the collapsible compass. The straightedge is a tool that has no curves. It is used to draw straight line when knowing two points. (Princeton) The only difference between a straightedge and a ruler is that a ruler has measurements while a straightedge does not. A carpenter’s square is two straight edges connected to look like an “L”. This tool allows others to construct right angles. (Princeton) Finally mirrors are used to see an object’s reflection. These tools have been used for years to make the construction of geometric shapes easier. (Princeton)
A compass is used to draw a circle using the center of the circle and a point on the circle as well. The two most well-known compasses are the modern and the collapsible. (Princeton) A modern compass is a device with two legs that are joined at one end. One of the legs is used to hold the compass to the paper while the other is used to create the circle on the paper. (Princeton)To use this instrument, you rotate it by holding the top of the compass where the two legs are joined. The leg that is used to hold the compass onto the paper is stationed at the center of the circle. (Princeton) The distance created between the two legs is known as the radius of the circle. The modern compass will stay the same distance unless by hand you make the legs wider or shorter. This feature allows is to replica the same circle multiple times extremely eas...
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...n compass as well as a collapsible compass. (Peil)
In conclusion, even though it was thought that a collapsible compass could not do the same as modern compass, it was false. A collapsible compass can do the same constructions but it may just take longer and be more difficult. A modern compass is used mainly today because of how simple it is. One is able to make a construction then pick up the compass and make the same one. It is able to keep the same diameter until manually changed. The straightedge and the compass are two tools that have been a big part of geometry and will continue to be.
Works Cited
"Compass and Straightedge Constructions." Princeton University. N.p., n.d. Web. 20 Mar. 2014.
Hartshorne, Robin. Geometry: Euclid and beyond. New York: Springer, 2000. Print.
Peil, Timothy. "Rusty Compass." Rusty Compass. MSU Moorehead, n.d. Web. 20 Mar. 2014
on this built in compass sense to guide them in the open ocean. Another use for
The other skill that Vikings excelled at was the skill of navigation. Their longships were the cutting–edge technology at the time, and their ingenious sun-compass, which worked somewhat like a sundial, allowed them to sail to their destination with precision. The longships were usually made with oak boards stripped from trees with thin ropes soaked in pitch trapped between joints to act as a flexible, waterproof membrane. These ships, combined with their streamlines design, are very fast and seaworthy and would flex out of places when a sturdier ship would shatter. The sun compass is also very useful because it is the only directional tool at the time. It uses a shadow cast by a small pin in the middle of a round plate with bearings to give the direction. This tool allowed them to sail on open seas without landmarks for directions, a great advantage. This tool allowed them to sail on open seas without landmarks for directions, a great advantage.
Euthyphro, is one of the many dialogues that was written by the Greek philosopher Plato dicussion the quest for wisdom by his mentor, Socrates. The time that The Euthyphro takes place is doing the time of a trial that Socrates is in regarding some here say that he was corrupting the youth of Athens, and ultimately leads to his demise. It is very important issue due to the system Socrates used to try to understand wisdom, and gives some input on his and Plato's view on holiness altogether. In all, the Euthyphro is a view of how the Socratic way of getting wisdom works and it enters into what Socrates and Plato define holiness as.
Heavenly navigation techniques, that are used in the site of sun and stars in the sky, along with knowing that the earth is a spherical, which astronomers used as a beginning to be executed by sailors that was in Columbus time.
Geometry, a cornerstone in modern civilization, also had its beginnings in Ancient Greece. Euclid, a mathematician, formed many geometric proofs and theories [Document 5]. He also came to one of the most significant discoveries of math, Pi. This number showed the ratio between the diameter and circumference of a circle.
One reason the compass is so important is because it helped sailors navigate their way across the seas and lands. According to Journey Across Time, “About 1150 Chinese sailors began using the compass to help them find their way. This lets ships sail farther from land.” (page 420) This stated that without the compass Chinese sailors wouldn’t have been able to find their way across the sea and discover many parts of the world we know of today. Ancient China Inventions also thought the invention of
... and the armillary sphere. The astrolabe and armillary sphere was used to study the skies and calculate the calendar for the date and their location. The Astrolabe was like a smartphone that contained a calendar and a map. Without theses inventions, constellations, maps, and calendars may not be used today. Without a guide of the stars and sky, there would be no NASA, to conquer the moon and no airport, to help the humans travel through the sky. Even though the early inventions couldn't take the Muslims traveling the sky, they were able to travel the sea and land. Document nine shows that Muslims were able to explore the world and conquer many lands and the seas around. Because they could travel lands and seas, they had a great trading network. Because they traded, their customs and knowledge were traded too. Resulting in the long lasting influence of the Muslims.
In the book “Phaedo,” Plato discusses the theory of forms with ideas that concern the morality of the form. There are four philosophers that are expressed which are Phaedo, Cebes, and Simmias regarding the execution of Socrates. Socrates is presented in “Phaedo” on the morning of his execution where he is being killed. He tells his disciples Simmias and Cebes that he is not afraid of dying because a true philosopher should welcome and look forward to death but not suicide. A man should never commit suicide. He says that we are possessions of the Gods and should not harm themselves. He provides the four arguments for his claim that the soul is immortal and that a philosopher spends his whole life preparing for death.
Thousands of years ago, ancient people looked up at the night sky and spotted unfamiliar objects in the sky, known as stars. Some people saw the stars as a tool to navigate at night and to keep up with the seasons. Others were completely clueless about what the stars were and why there were up in the sky. This eventually led to curiosity and the beginning of astronomy. The very first astronomers grouped stars into constellations, which basically is connecting the stars to make an imaginary outline of people, object, or animals. This allowed the astronomers to keep track of the movement of the planets and the sun, which allowed them to create the very first accurate calendar to know when it was the right time to harvest and plant.
To understand the logic behind Plato’s Tripartite theory it is important to recognize that his theory is just drawing comparisons from how societies operate and how human beings operate. What Plato is discussing with this theory is how a just society would operate as compared to how a just person would operate. He explains that just like society is split up into different institutions, such as the ruling class and the working class, the human being is also split up into different institutions. Plato describes this tripartite separation by using an allegory of a charioteer driving two horses. The charioteer signifies the rational part of the soul. The foul black horse signifies the appetitive part of the soul and the white noble horse next to it signifies the spirited part of the soul. This white horse shows characteristics such as love, modesty, and restraint. On the other hand, the black horse has characteristics such as insolence and pride. While the charioteer is the one holding the reins, he is overcome by the black horse and the white horse as they try to push him into different directions. The white horse works to keep its counterpart in check but, as Plato describes in Phaedrus, the black horse who is steering towards the desires of the individual is the one who takes control in the end.
Empedocles was born in Acragas, Sicily about 492 BCE to a distinguished and aristocratic family. His father, Meto, is believed to have been involved in overthrowing Thrasydaeus who was the tyrant of Agrigentum in the year 470 BCE. Empedocles is said to have been somewhat wealthy and was a popular politician and a champion of democracy and equality.
one with a radius of 12cm. The cones will be made by using a compass
I have conducted my research through interview with someone familiar with construction and development as how geometry is used in these fields.
Compass is a basic geometrical tool with two arms and looks like an alphabet “V”. One arm carries needle and the other arm contains a pen or pencil with an adjustable screw. The pointer represents the center of the circle.
Euclid of Alexandria was born in about 325 BC. He is the most prominent mathematician of antiquity best known for his dissertation on mathematics. He was able to create “The Elements” which included the composition of many other famous mathematicians together. He began exploring math because he felt that he needed to compile certain things and fix certain postulates and theorems. His book included, many of Eudoxus’ theorems, he perfected many of Theaetetus's theorems also. Much of Euclid’s background is very vague and unknown. It is unreliable to say whether some things about him are true, there are two types of extra information stated that scientists do not know whether they are true or not. The first one is that given by Arabian authors who state that Euclid was the son of Naucrates and that he was born in Tyre. This is believed by historians of mathematics that this is entirely fictitious and was merely invented by the authors. The next type of information is that Euclid was born at Megara. But this is not the same Euclid that authors thought. In fact, there was a Euclid of Megara, who was a philosopher who lived approximately 100 years before Euclid of Alexandria.