Pure mathematics

Reflection on True or False Equation Routine After watching the True or False Equation Routine, I have concluded that each one of the NCTM Process Standards was met throughout the video. During the video, students used communication to explain themselves and their thought process. Students had to organize their mathematical thinking and could do this through partnered discussions and whole group discussion. The second standard that this video met was reasoning and proof. I noticed that each…

who was believed to have been born even before Socrates (who was born on 469 BC). His Birthplace is in Italy. The word 'Paradox' is a statement that apparently opposes itself (in terms of meaning), but may be still true(by thinking in terms of Mathematics and it's methods). Thus it might be invalid most of times but however it helps in developing one's way of perceiving things and thus improves our critical thinking. Zeno of Elea offered arguments that led to conclusions contradicting what we…

(3) Equation (3) gives limit moment about 11% higher than equation (2) regardless of h. One notable point is that the above solutions depend only on bend factor(h), not on r/t and R/r. Equations (1-3) are applicable only for the pure in-plane bending moment and the effect of internal pressure is not taken in to account. Also these analytical solutions consider constant wall thickness along the contour of the pipe bend cross section. However, the most of the pipe bends are made using a forming…

at school, math and science were my favorite subjects. I was really good at math and science subjects, enjoyed solving math problems, and would easily understand mathematic and scientific ideas and lessons. On the other hand, I witnessed that most girls dealt with mathematics and scientific lessons in a different way. They hated mathematics and didn’t enjoy solving math problems like I did. Instead, they were more interested to literature and social sciences. As I grew up, I also came to believe…

Nowadays, the majority of college students have a wish to make successful carrier in maths field. But, lack of sufficient math knowledge and proficient skills, these kinds of learners feel difficulty in facing their final mathematics exam. College math problems are common in students since long time. That is why a large number of pupils need perfect college math help for their final exam and a bright future. According to specialists, every student studies in a different way and there is not…

THE SINE FUNCTION (SIN) Sine function is an odd function. Trigonometric Ratios in a Triangle Definition of sinα in a Triangle is the following statement: For any acute angle α, we draw a right triangle that includes α. The sine of α, abbreviated sin α, is the ratio of the length of the opposite this angle to the length of the hypotenuse of the triangle. If we simplify we get a formula which says: It is shown in a diagram below. We can see immediately that this definition has a weak point. It…

“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality.” By Richard Courant. Mathematics is not just a mere subject which only consists of numbers but a universal language. Mathematics can be defined as “the study of relationships among quantities, magnitudes and properties, and the logical operations by which…

Ant colony algorithm has three steps: pheromone initialization, building tour, updating pheromone.For the ant colony algorithm, path selection influence a little by the pheromone initialization. In order to get a better result, the pheromone value is always initialized slightly higher than the one released in each iteration.We have taken the initial value of pheromone as τij(0)= m/Cmin where , τij(t) is the residual pheromone on the path between node i and node j at moment t. m is the number of…

Basic skills, as defined from the book Teaching the New Basic Skills: Principles for Educating Children to Thrive in a Changing Economy, are those skills that are fundamental in reading, mathematics, solving semi-structured questions where assumptions should be developed and experimented, working and communicating effectively with different kinds of people, and accomplishing simple tasks via computers (Murnane & Levy, 1996). However, according to Kimberly Lightle, Director of the Office of…

If R and r is the Circumradius and Inradius of a non-degenerate triangle then due to Euler we have an Inequality stated as and the equality holds when the triangle is equilateral. This ubiquitous inequality occurs in the literature in many different equivalent forms [4] and also Many other different simple approaches for proving this inequality are known. (some of them can be found in [2], [3], [5], [17], and [18] ). In this article we present a proof for this Inequality based on two basic…