Students' difficulties in similar triangle questions

Similar triangles in questions are usually given as separate, adjacent or overlapped. Furthermore, similarity types such as Side-Angle-Side (S.A.S.), Side-Side-Side (S.S.S.) and Angle-Angle (A.A.) are requested in the questions. Students have more trouble in other types of questions. The purpose of this study is to investigate the difficulties of students about similar triangles and the reasons for these difficulties. This research was carried out with the case study method, which is one of the qualitative research approaches. The study was conducted with 55 Science High School 9th grade students and 9 open-ended questions were used to examine students' knowledge about “similarity in triangles”. Furthermore, 5 students were interviewed to find out the reasons for their solutions. Descriptive analysis method was used to analyze the data. As a result, it can be concluded that students have difficulties mostly in overlapped triangles and Angle-Angle type questions. On the other hand, it can be concluded that students are quite successful where similar triangles are given separately. In the light of the findings obtained in this study, it can be advised for lecturers to focus on the questions where similar triangles are overlapped while explaining the similarity in the triangle. Keywords: Similarity, Triangles, Difficulties, High School Students.

Dilations and the Equation of a Line

Track students' understanding of proportional reasoning by combining transformational geometry, similar-triangle reasoning, and linear relationships.

Analysis and Calculation of Transmission Ratio of Simpson Planetary Gear Mechanism Based on Velocity Graphic Method

The paper summarizes the principle of applying velocity graphic method to analyze Simpson planetary gear mechanism, which provides guidance for analysis procedure. The movement of each element in the mechanism can be intuitively understood through drawing the linear velocity vectors of three constant velocity points. The similar triangle principle is used to calculated transmission ratio of each transmission scheme in the linear velocity vector diagram, and the correctness of the analysis method and process is verified by the transmission ratio calculated by velocity graphic method and analytic method.

Solution Classification for Perspective-Three-Point Problem Base on PST Method

The perspective-n-point (PnP) problem is originated from camera calibration. It is to determine the position and orientation of the camera with respect to a scene object from n correspondent points. And a new stable algorithm by using a geometric constraint called perspective similar triangle (PST) can give new equations to solve P3P. The PST method achieves high stability in the permutation problem and in presence of image noise. Using the complete discrimination system, we obtain the solution classification of the new equation for the P3P problem. The solution classification gives a set of formulas to determine the number of real solutions to the P3P problem. Based on the formulas, we may know whether the parameters give multiple solutions or not and are critical or not which is very important to present robust algorithm.

The Three Stooges Meet the Conic Sections

Students analyze a photograph to solve mathematical questions related to the images captured in the photograph. This month, a still from a Three Stooges movie is analyzed. The mathematics involves conic sections, implicit differentiation, similar triangle geometry, and scaling factors

A STABLE DIRECT SOLUTION OF PERSPECTIVE-THREE-POINT PROBLEM

The perspective-three-point problem (P3P) is a classical problem in computer vision. The existing direct solutions of P3P have at least three limitations: (1) the numerical instability when using different vertex permutations, (2) the degeneration in the geometric singularity case, and (3) the dependence on particular equation solvers. A new direct solution of P3P is presented to deal with these limitations. The main idea is to reduce the number of unknown parameters by using a geometric constraint we called "perspective similar triangle" (PST). The PST method achieves high stability in the permutation problem and in the presence of image noise, and does not rely on particular equation solvers. Furthermore, reliable results can be retrieved even in "danger cylinder", a typical kind of geometric singularity of P3P, where all existing direct solutions degenerate significantly.