This thesis presents a modi_cation of the third-order Runge-Kutta method based on the convex combination of the Lehmer mean, and its local truncation error. Stability analysis of the proposed methods show that the stability areas of the discussed method are the same as the stability area of the third order Runge Kutta method based on the arithmetic mean. Then the discussed methods are applied t…
Menelaus' theorem basically applicable for triangles. Some authors have developed it in quadrilateral. This thesis develops Menelaus' theorem for the pentagon. The prooving process is done in a very simple way that is by using Menelaus' theorem on the triangle by partitioning the pentagon into several triangles, area comparison of the triangle, and similarity. The results obtained are the _ve p…
This thesis discusses the development of the Ceva’s theorem on the pentagon in various cases including for the convex pentagon and the nonconvex pentagon. The Ceva’s theorem discusses the case of one-point concurrent in the pentagon. The prooving process is done in a simple way that is by using area proportion. The results obtained from this thesis are the existence of five lines from each …
Stirling numbers are divided into two types namely Stirling's numbers of the _rst kind s(n; k) and Stirling's numbers of the second kind S(n; k). The tribonacci number is a generalization of a Fibonacci number which has a unique and eisily recognizable shape, since each subsequent tribe is obtained by summing the three previous tribes beginning with the tribes 0, 0 and 1. Stirling's matrix of t…
One of generalisation of Fibonacci sequences is the -Fibonacci. This sequence can be constructed by Pascal 2-triangle. -Fibonacci sequences if operated in modulo arythmatic can produce a unique sequence that is the recurring numbers. The repetition of thus numbers is called Pissano Period Length, denoted by . The -Fibonacci sequences have the same period length if and . So, we can produce new f…
The purpose of this study is to explain the techniques in detecting the outlier of the ordinal data by using the regression coefficients. Identification data derives from the sport tests of Junior High Schools Students (SMP) in Pekanbaru. The ordinal logistic regression is combined with the proportional odds model. As the attraction of the modulus ordinal regressions interest, the jackknife tec…
Morley’s Theorem generally applies in a triangle. In this thesis Morley’s Theorem is proved in a quadrilateral and special rectangles and also the side length of Morley’s quadrilateral is determined. Quadrilaterals discussed in this paper are square, rectangle, rhombus, kite and isosceles trapezium. Simpler ways are used to prove by applying congruence concept and trigonometric concepts. …
The tetranacci number is a generalization of Fibonacci numbers whose form consists of the sum of the four previous term having begin with 0, 0, 0 and 1. Pascal’s triangle shape is geometrically obtained from the coefficients of the powers of summation of the two numbers, i.e. can be arranged in the from of a triangle. The numbers that exist in every row of the Pascal’s triangle is the coeff…
This thesis discusses a problem in the management of blood supply chain at the blood banks with perishability characteristics especially for the red blood cells and platelet. Focus of this discussion is to minimize the total cost, shortage and wastage levels of the blood unit. Stochastic integer programming approach is used to solve this problem by the following assumptions blood group and some…
This thesis discusses Napoleon's Theorem at hexagon having three pairs of parallel sides in same lengths with two cases (i) regularly built toward outside and (ii) regularly built toward inside. Provided proofs use the congruence and trigonometric concepts. At the end of the discussion, the development of Napoleon's Theorem by using geogebra applications is presented. Keywords: Napoleon's The…
This Thesis Discusses The Modifications Of Van Aubel’s Theorem On A Triangle, That Is The Line Drawn From The Triangle Vertices To The Quadrilateral Vertices, The Line Drawn From The Midpoint Of The Sides Of The Triangle To The Intersection Point Of The Diagonals Of A Square, And The Line Drawn From The Midpoint Of Vertices Of Two Squares To The Vertices Of The Triangle. From The Modification…
Extreme rain phenomenon is one of the most interesting climate changing issues to be studied, especially about the risks posed by these phenomenon, including the danger of floods, landslides and the collapse of water dams. Early recognition of extreme rain patterns and ability to estimate extreme rainfall in the future will reduce the risk of negative impacts from extreme rain phenomenon. Patte…
The sequences of pyramid is a number of sequence obtained based on the arrangement of integers in the pyramid. Some criteria of sequences can be formed such as a sequence obtained from the number of numbers at an angle, the number of numbers on the base of each level and the number of numbers on the pyramid surface. If the numbers on each corner of the pyramid are arranged will produce a sequen…
The quadrate equation can not only be solved by using the formula that exists in a high school math book. Through the concept of factoring, the concept of addition of roots, and the theorems developed by W.A Donnel other methods can be determined to solve quadrate equation. Next, use a rectangular box consisting of three rows and three columns, two of which contain the coefficient value a and t…
In the development of science and technology, sequence and series become very important and useful in various fields. This thesis reveales how to obtain the general form of a series of integers of numbers which is denoted n m i  i 1 by determining the sum formula formed from m  9 . The formula of the sum of the n-terms obtained is listed in a table and it is sorted from the hig…
This thesis discusses the quotient remainder of   n m i  i 1 13 divisible by two, three and five by using divisibility concept. This is done by listing the residual of result division into a table form for analysis. Further it is showed that   n m i  i 1 13 is a linear combination of   n m i  i 1 2 and   n m i  i 1 3 ,   …
This thesis discusses the identity of Fibonacci, Lucas, and tribonacci numbers in modulo 6, and their relation with Fibonacci, Lucas, and tribonacci numbers in modulo 2 and modulo 3. Discussion of Fibonacci numbers identity, Lucas numbers and tribonacci numbers in modulo 6 utilize a method of Layendekkers and Shannon [Notes on Number Theory and Discrete Mathematics, 19 (2013), 66-72]. Fibonacci…
A triangle has special lines, such as angle bisectors and perpendicular bisector. These special lines are concurrent with their corresponding concurrent points, and called incenter, excenter and circumcenter. This thesis discusses how to compute the radian of Sawayama-Thebault’s circle using trigonometry and area of a triangle, i.e. r1 = (L/a)(1 − βτ )(1 + γτ ) and r2 = (L/aτ 2)(τ + �…
This thesis discusses the modification of double midpoint rule and corrected midpoint rule by adding the derivative evaluated at arithmetic mean of the nodes to approximate a definite integral. The proposed rules give increase of precision over the existing rules. The numerical results show that the proposed rules gives a smaller than the existing rules. Keywords: Midpoint rule, numerical inte…
This thesis studies the development of Kosnita’s theorem using incenter and centroid, that is by means of using them as an initial construction in a triangle. There are three constructions produced, i.e. incenter-circumcenter, incenter-centroid and centroidcentroid. The concepts of congruency, incenter and centroid concepts are used to make the construction so that, with these simple geome…