Hyperbolic geometry

Since the beginning of our time together as a class, we have held many late night discussions on what geometry instruction may look like at the elementary level. I have learned about the Geometric Habits of Mind that should be present in our classrooms as we engage our students in geometric thinking. I have also had demonstrated for me what it looks like for a teacher to help his/her students move forward to higher Van Hiele levels of thought. These two systems of thinking, along with the…

My chosen area of mathematics is angles in polygons, due to the visual nature of geometry enabling the students to be engaged and stimulated (Chambers & Timlin, 2013). Not only this, but since geometry is present in our everyday lives, students have a basic grasp of shapes, however, they have not developed a critical understanding of what properties define that shape (Bell et al., 1983). This basic foundation knowledge can also cause difficulty when it comes to teaching and learning as the…

The mathematic classes I teach at the high school are one section of Advanced Mathematics, two sections of Algebra 1, two sections of high school Pre-Algebra, and one section of eighth grade Pre-Algebra. The other two mathematic teachers cover Geometry and Algebra 2. These teachers also teach science classes, so I am the only fulltime mathematics teacher. Within the junior/senior high building, there are 80 junior high students (seventh and eighth grade) and 150-200 high school students…

CTET FEB (2016) - PAPER 2 SOCIAL STUDIES 44. (4) Famous Indian mathematician Aryabhata wrote the famous Aryabhatiyam book. The Aryabhatiyam is reference manual for mathematics and many of its facts and figures are still used in the modern society. The book was written in Sanskrit language and comprises 121 verses. 45. (2) Lord Buddha delivered his first lesson at Sarnath to his five beloved disciples (name). The very first lesson delivered by Lord Buddha is popularly known as Dharmachakra…

The journey Donald Duck is taking in this short film tells the origins of mathematics and how mathematics can be found in everyday life. The film shows you how it all began by taking Donald back to ancient Greece. Pythagoras is the father of mathematics and he showed us how everything does in fact include math in it. Pythagoras learned that from taking one thread of string and dividing it in half then dividing that in half and so on, he learned they each have their own tones due to each length…

This math challenge was easy to approach, because I realized that the lines O1O, O1O2, and O2O1, form a triangle, I realized that if that triangle was a right triangle I could find the distance between O1, and O. To prove that triangle OO1O2 is a right triangle I used the radii of O1, I realized that the sides of triangle PO1Q, O1P, and O1Q, are radii, and therefore they are equal. Since they are equal, the triangle PO1Q, is an isosceles triangle. In an isosceles triangle the base angles are…

is also used in Euclidian Geometry. “A” squared plus “B” squared equals “C” squared is the formula used in the theorem. For example, we are given two numbers in the sides of a triangle; if we are given the adjacent and opposite sides, and we must figure out the hypotenuse, we will be required to use the Pythagorean Theorem. The two numbers given are squared, and our third number, we obtain it from the sum of the two numbers squared. Pythagoras’s theorem applies to geometry; however, it can…

Figure 2.1 is a polygon with 12 sides. The polygon is not convex, as there is at least one reex angle. The objective of the art gallery problem is to hire the most efficient number of guards required to have vision of each point inside of the polygon. Begin with the process of vertex guards. The most visually optimal way to prove the result _n 3 _ is by first triangulating the polygon. Every vertex of the polygon can be attached in such a way that the entire polygon is made up of solely…

Pythagoras is a greek mathematician and astronomer. He is best known for the Pythagorean theorem but is also known for other math related theories. He founded a group called the Pythagoreans, who also are credited to math related theories. He also has many astronomical theories, some proven and some disproven. Pythagoras was born around 570 BC in Samos, Greece. His dad was a traveling merchant, so his mom had to raise his siblings and him by herself most of the time but Pythagoras did travel…

he wanted his son to follow in his footsteps. The reason that he didn’t was Bernoulli saw his mathematical potential and advocated for him to become a mathematician. Leonhard Euler didn’t just help in one specific part of math he helped in geometry, calculus, trigonometry, algebra, number theory, physics, lunar theory and astronomy. He is responsible for the function f (x),…