In general, a lot of discussion on the line discusses the symmedian point. This thesis discusses the reflection of trimedian and trisector. The discussion is about the side lengths of the symmedian and the area of the symmedian of triangle. The proof is done using a very simple method, namely by using the concept of the height line on the triangle and the trigonometric concepts of the trian…
This thesis discusses the comparison of the area of the symmedian triangle with the original triangle. This thesis also discusses determining the area of the median triangle and the area of the bisector triangle. Calculation of the area of a symmedian triangle and bisector triangle using trigonometry. Calculation of the area of a median triangle using Varignon theorem. Furthermore, compare…
This thesis discusses the modification Varignon Theorem on quadrilaterals with dividing the sides of the quadrilaterals into thirds, four and five parts and determining general formula if the side of the quadrilaterals is divided into n parts. The proving process is done in a very simple way, namely by using the similarity between two triangels, ratio and the sequence of numbers.The result …
This research aims to produce mathematics learning tools in the form of syllabus, lesson plans (RPP), and student worksheets (LKPD) based on learning models based on the problem of building flat side spaces for 8th grade students of junior high school. This research uses a 4-D development model which includes four stages, namely: (1) define (defining); (2) design (planning); (3) develop (d…
This research is to produce mathematics learning tools in the form of syllabus, lesson plans (RPP), and student worksheets (LKPD) based on the problem-based learning model of social arithmetic material for seventh grade students of junior high school. This study uses a 4-D development model which includes four stages, namely: (1) define (define); (2) design (planning); (3) develop (development)…
This research is motivated by teachers who still have difficulty in designing learning tools based on the 2013 curriculum. This study aims to produce mathematical learning tools based on a problem-based learning model to facilitate valid and practical mathematical communication skills of students. Learning tools developed in the form of a syllabus, lesson plan (RPP), student worksheets (LAS). T…
This research was motivated by the mathematics learning outcomes of grade VIIIB students of SMP IT Darul Huda Ukui which were still below the Minimum Completeness Criteria (KBM) with a percentage of 37,03% who reached the KKM in circle subjects. Build flat side space. The purpose of this study aims to improve the learning process and improve students' mathematics learning outcomes through the a…
This research is motivated by the 2013 Curriculum which requires students to be active in learning so that they are able to build their own knowledge and be able to solve contextual problems that facilitate mathematical problem solving abilities. The purpose of this research is to develop learning tools in the form of syllabus, lesson plans, and LKPD using the Problem Based Learning (PBL) …
This final project discusses combinations of Newton-Halley method for solving nonlinear equations. This method is obtained by modifying Taylor expansion, Newton method and Halley method. The convergence of the proposed method is proved analytically that the method has sixth order of convergence and their efficiency indexes are 1.431. At the end of the discussion, computational results of c…
This final project discusses about the dynamic behaviors of a Lotka-Volterra predator-prey model with predator cannibalism. The observed model consists of four equilibrium points. Simulation of the model is carried out with spesific parameters to describe the behavior and stability of the equilibrium points. Based on results of simulation, cannibalism has positive or negative effect depends…
This final project discusses about the predator-prey model with harvesting rate on predator. This model also use Holling II function. The model has three equilibrium points in which they are unstable. Simulation of the model is carried out to interpret the relationship between predator and prey . This is a review of Triharyuni and Aisyah [IOP Conference Series: Earth and Enviromental Scien…
This nal project discusses the pristine numbers. Pristine numbers can be determined by recursive divisors function. Using the recursive rule method in recursive divisor function, then it can be determined the pristine numbers form. A number is pristine if a(n) = n where a(n) recursive divisors function of n. The result of pristine numbers form are 2c; 2cq; 2cqr; 2cq2; 2cqrs; 2cq2r. This is…
This final project discusses the constancy of Haruki’s entry on the ellipse. Given two nonintersecting chords AB and CD on the ellipse and a point P on the arc AB remote from points C and D, let E and F be the intersections of chords PC,AB and PD,AB respectively. The value of AE · BF/EF does not depend on the position of P. The proof is presented by geometric transformations, using the …
This final project discusses the MERS-CoV Spread Model with a concentration of Dipeptidyl Peptidase 4 (DPP4). This model uses a system of nonlinear differential equations with four compartments, namely virus-free cells, virusinfected cells, free virus and DPP4. The observed model consists of two equilibrium points, namely the free point and the infected equilibrium point. The stability ana…
The purpose of this research is produce mathematics learning devices in the form of syllabus, lesson plans and LAS based on Problem Based Learning to facilitate mathematical problem solving ability that met the valid and practical requirements for comparative material class VII. This research is development research method using a 4D ( define, design, develop, desseminate stages). The main rese…
This research is motivated by the low mathematics learning outcomes of students because students have difficulty understanding mathematical concepts and students are less active in the learning process. So we need a learning model that can help students learn and can stimulate students to understand concepts to complete mathematics, one of which is the application of the Problem Based Learning …
This research is a research and development aims to produce a syllabus, lesson plans (RPP), and student worksheets (LKPD) with a problem based learning model to facilitate mathematical problem solving ability for Senior High School grade X on the material Three Variables Linear Equation System. This research and development uses 4-D development model. The instrument used in the research was val…
One of the main focuses of mathematics learning objectives is that students master mathematical problem solving skills (KPMM), but it is known that KPMM of students is still quite low and teacher learning tools cannot be said to facilitate this ability. This research is intended to produce learning tools consisting of syllabus, lesson plans and LKPD based on Problem Based Learning to facilitate…
This research is a development research which is motivated by the low mathematical problem-solving ability of student. This research aims to produce a mathematical learning device based on problem based learning to facilitate nineth-grade student of SMP/MTs mathematical problem solving ability of valid and practical on transformation material. The development model used is the 4-D model which c…
This nal project discusses the solution of travelling salesman problem with multiple objective functions in the form of triangular fuzzy. Triangular fuzzy numbers are converted into paramaters. Moreover the fuzzy numbers in the form of parameters are converted into the form of a convex combination. Optimal solution of the single objective function travelling salesman problem provides the …