Euclidean space

In this project I will talk about curves in three space, also known as curves in three dimensional space or 3 - D. Many of us are familiar with two dimensional space or 2- D. It is called two dimension space because it has two axes: the x-axes and the y-axes. Three dimensional space is represented by the symbol it is called three dimensional space because three axes are used to draw, and the three axes are: x, y, and z. Figure 01: Standard axes of 3 dimensions This is the standard axes of three dimensional or 3- D. Most of the time it only shows the positive value, though the negative value can be added. Three dimensional space use almost the same formula that is used in two dimensions. The formula that we use in two dimensions has…

aggressiveness. It is also considered to ensure that the fish have the right surroundings they have adapted to, whether it's driftwood to hide in or rocks and small cave like structures the fish can lay in. At Aksarben Aquarium they make sure to put the right fish in the right tanks so that the fishes needs are met and are kept from any harm. It is very important to consider the needs of a fish before throwing it into a random tank, compatibility is the key. The introduction of a new species…

This morning we are going to play a little game. I have three cups here and a marble. Keep your eyes on the marble. When I am done mixing up the cups, I will ask you to guess which cup the marble is hidden under. (Don’t tell the your going to put the marble under the cup just let the assume you will be putting it under.) Place all three cups on a table upside down. Pretend you will be placing the marble under a cup. To do this, lift the cup up from the back, put your hand under the cup like…

have pushed Lobachevsky’s research towards exploring the possibility of non-Euclidean geometry, although this seems rather far fetched as the two had never actually corresponded. [3] Lobachevsky became enthralled by mathematics, becoming a professor in the field, and ultimately a rector of the college. He enjoyed a relative fame in the mathematical community, publishing not only in Russia, but also Germany and France and eventually being awarded a medal by Nicolas the second. In 1832 Lobachevsky…

asymmetric tiles which then are possible to tessellate, every single one in a different way. Escher used 27 out of these 28. Tessellations have two definitions. One is, “A plane tessellation is an infinite set of polygons fitting together to cover the whole plane just once, so that every side of the polygon belongs also to another polygon. No two of the polygons have common interior points. (Cornell)” and the other is, “ A tessellation is called regular if its faces are regular and equal. The…

I used to believe that geometry wasn’t possible without algebra, that geometry was essentially a representation of algebra. I didn’t have an experience of geometry that focused on the creativity and ingenuity that I’ve come to now know. Chapter 6 of Journey Through Genius reiterates how impressive the discipline of geometry truly is. Cardano’s solution to the general solution was astonishing, to me, because of the literal use of geometry to find the appropriate algebraic identities and the…

Phenomena, Data, and On Division of Figures are some of Euclid's other works. In his work Optics, Euclid tries to prove that that sight was created by rays coming from the eye, instead of light entering the eye which was a common belief in that time. In Optics, Euclid also comments more on perspective. Phenomena is about planetary motions, and Data is about finding measurements and quantities when others are given. Euclid is extremely important to mathematics, even though it is misunderstood…

Buried Treasure Ashford University MAT 221 Buried Treasure For this week’s Assignment we are given a word problem involving buried treasure and the use of the Pythagorean Theorem. We will use many different ways to attempt to factor down the three quadratic expressions which is in this problem. The problem is as, ““Ahmed has half of a treasure map, which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of…

Whether someone partakes in the activities of a church or are atheistic, religion touches all of us. Our understanding of how our morality are formed is debateable, with how close an individual’s ideals are connected with their religion’s commandments it is reasonable to believe that there is some connection between the two. To claim that someone does not have ideals, that they cannot think for themselves of what they think is right and wrong is to many, a ridiculous statement which in hand is a…

Leonhard Euler lived form 1707-1783. During his life time he published eight hundred sixty six pages and books to only be surpassed by Paul Erdos later on. His complete work is ninety volumes. Remarkably, most of his outputs were from his last two decades of being alive while his completely blind (www.usna.edu). His most famous contributions to the world of mathematics was his equation or better known as the Leonhard equation which is V+R-L=1. Where V is equal tothe number of vertices (nodes)…