This thesis discusses the area of the outer Napoleon and the outer semi Napoleon in triangle and special quadrilateral. The area of the outer Napoleon in a triangle constructed from an arbitrary triangle and the area of the outer Napoleon in a quadrilateral are constructed from rectangles that have two parallel sides including rhombus and parallelogram, while the area of the outer semi Napoleon…
Morley’s theorem is applied using inner angles on triangles and squares, in this paper will be developed Morley’s Theorem Using the outer angle on triangles and squares (rhombus, isosceles trapezoid and kite). In any triangle, the Morlay theorem using an outer angle produces an equilateral triangle, the rhombus produces an the rectangle, the isosceles trapezoid pro duces an the kite an…
Derivative of function is one of the topics in the mathematics book in Se- nior High School (SMA). In some textbooks used by students, there is no general form of the nth derivative of the function h(x)/f (x) or h(x)/√f (x). This thesis discusses how to obtain the general form of thenth derivative func- tion 1/(ax + b), (ax + b)/(cx + d), 1/√ax + b, and (ax + b)/√cx …
Fibonacci sequence is defined by Fn = Fn−1 + Fn−2 for n ≥ 2 with F0 = 0 and F1 = 1. Lucas sequence is defined by Ln = Ln−1 + Ln−2 for n ≥ 2 with L0 = 2 and L1 = 1. While Fibonacci-Like sequence is a generalized of Fibonacci and Lucas sequence that defined by Sn = Sn−1 + Sn−2 for n ≥ 2 with S0 = 2 and S1 = 2. The Fibonacci-Like sequence forms the sequence numbers 2, 2…
This study presents the n/2th derivative of sine function f (x) = sin px and cosine function f (x) = cos px where p is a positive integer and x is a variable. The n/2th derivative is a fractional derivative of an arbitary order. The fractional derivative can be obtained by using Riemann-Lioville integral fractional definition that is closely related to gamma functi…
This article discusses an iterative method to solve a nonlinear equation, which is free from derivatives, obtained by approximating a derivative in the method proposed by Rhee et al. [Int. J. Comput. Math., 95 (2018), 2174-2211] by the method of divided difference. We show analytically that the method is of order eighth and for each iteration it requires four evaluation functions. Numeric…
Wind speed is the airspeed moving horizontally at a height of two meters above the ground. This study aims to obtain the best wind speed model in Peka- nbaru. Monthly wind speed data from 2008 to 2017 are used in four wind speed models in the form of mixed probability density functions, that are Lindley distribution, Akash distribution, Shanker distribution, and Sujatha distribution. The maximu…
This thesis discusses the development of nutrition optimization model using goal programming to satisfy daily nutrition needs of adolescent. Objective function is designed to minimize deviations from the nutrients according to recommended daily nutrition needs. Nutrients needs are determined according to Indonesian Recommended Dietary Allowances (AKG) incorporated as goal constraints. This thes…
This study uses air pollution data with particulate matter 10 (PM10 ) pollutants in the Pekanbaru city in 2009 2015. Air pollution data was analyzed to obtain probability model for air pollution in the Pekanbaru city by using the Dagum distribution. This distribution is a special form of generalized beta II distribution with 3 parameters, namely b as a scale parameter and a, p as shap…
This thesis discusses the modifications of fuzzy algebra that are definition of positive and negative fuzzy number and arithmetic fuzzy number. Definition of positive and negative fuzzy number are obtained by comparing the area located on positive and negative x-axis. While, arithmetic fuzzy number is obtained using the formula of the multiplication of parametric function of fuzzy number. Modif…
In this Thesis the identity of k-Tribonacci numbers in modular ring Z6 and in modular ring Z8 are discussed and their relationship with the k-Tribonacci number of factors of 6 and the factor of 8 are analysed using the method carried out by Layendekkers and Shannon [Notes on Number Theory and Discrete Mathematics, 19 (2013), 66-72]. Our computational experiment results show that (i) for k ≡ 1…
This thesis discusses the solution of a dual fully fuzzy linear system with fuzzy trapezoidal numbers for positive fuzzy number solutions and negative fuzzy numbers. The general form of the dual fully fuzzy linear equation system is ˜ A⊗ ˜x⊕˜b = ˜ C ⊗ ˜x⊕ ˜ d. The general form of the fully fully fuzzy dual equation system is transformed into the form of ˜ A⊗˜x = ˜ C ⊗˜x⊕…
The identity of Fibonacci numbers and Lucas numbers in modulo 7 and modulo 8 can be determined using congruence in modulo tables. In Modulo 8 the relationship of Fibonacci numbers and Lucas numbers can be analyzed in modulo 2 and modulo 4. Fibonacci numbers, and Lucas numbers in modulo 8 can be obtained from Fibonacci numbers and Lucas numbers in modulo 2 and modulo 4. Twice Fibonacci numbers a…
The Cross’ theorem is basically for triangles. Some authors have developed in rectangles and used rectangles on side of triangle. This thesis discusses the modification Cross’ theorem on triangle which is expanded once more by constructing a square outside direction on each side of the Cross’ theorem triangle. The proof process is done in a very simple way using congruence. Besides, the m…
Tsunami is a series of ocean waves that can propagate at speeds of up to more than 900 km/hour. Aceh Province experienced an earthquake disaster on December 26, 2004 at 7:58:53 WIB with the power of 9 Richter scale. The earthquake in Aceh caused a tsunami disaster with a height of up to 30 m, and caused 250,000 deaths. This study has used data from the 2004 tsunami in Aceh. Tsunami wave height …
This thesis discusses two three-step iterative methods which are derived by combining the iterative methods that contain the function and first derivative with Newton’s method. The process of the combination uses the principle of an undetermined coefficient method by allowing only one additional function evaluation that may occur in the process. By combining the methods proposed by Khattri an…
The sequence of base plane on the heptagonal and octagonal is the sum of elements on the base of each heptagonal and octagonal pyramid level. This thesis constructs the form of the base sequence of each heptagonal and octagonal and the pyramid of sides by using a pattern of sequences formed on the base sequence tetrahedron,pyramid, pentagonal pyramid or hexagonal pyramid. Additionally, by regis…
This thesis discusses a formula to reconstruct the P-position of three-pile Fraenkel game by using mex operator. P-position is a dynamic position where a gamer can decide his victory. The result shows that P-position of three-pile Fraenkel game is a series (An;j ,Bn;j ,Cn;j), with the value of An;j is the smallest positive integer which does not exist in (Ai;j ,Bi;j ,Ci;j) with 0 ≤ i < n, whi…
The sequences of base side is sequences obtained from the arrangement of the number of integers in one of the base side of the pyramid space. This the- sis discussess the sequences of base side on heptagonal and octagonal pyramids pyramids base facests with making a three dimensional sketch and method of _nding the number pattterns formed on sequences base side of pentagonal, he xagonal, heptag…
In general the Van Aubel's theorem is constructed from any quadrilateral. Some authors develop the Van Aubel's theorem on any triangle. This thesis discusses another form of the Van Aubel's theorem on triangle. In this study the author makes proof by using congruence, similarity, and concurrent. The results obtained in this thesis are three pairs of parallel lines, equal in length and perpendic…