Some Properties of Cone Inner Product Spaces over Banach Algebra

The aim of this paper is to introduce a concept of a cone inner product space over Banach algebras. This is done by replacing the co-domain of the classical inner product space by an ordered Banach algebra. Some properties such as Cauchy-Schwarz inequality, parallelogram identity and Pythagoras theorem are established in this setting. Similarly, the notion of cone normed algebra was introduced. Some illustrative examples are given to support our findings.

Extended Pythagoras Theorem Using Hexagons

This article provides the geometric and algebraic proof of the variant equation of the Pythagorean theorem x^2-xy+y2=z^2 . The hypothesis that will be proven is that just as squares govern the original version x^2+y^2=z^2 , hexagons are found to govern x^2-xy+y^2=z^2 . Both the special case x=y  and general case of x≠y  are examined.

Validation and Implementation of Hawgent on Pythagoras Theorem

Math lessons are abstract and complex for students to understand, so that the teachers need instructional media to develop by using technology to help their students get deep learning. This study aimed to validate the instructional media to teach the Pythagorean theorem and describe the students and the teachers’ responses to the instructional media. The researchers implemented the ADDIE model in this study. The sample comprised 30 students in 7th grade and 56 teachers. The process of validation involved ten academics. The results of this study showed that the instructional material could be used. The results also showed that the students were happier when the teachers used the instructional media in the classroom.

Discovery Teaching about Calculating Side Lengths of Right Triangles Using Pythagoras Theorem with the Help of Geogebra Software

Discovery teaching is an active teaching method that encourages learners to create their own knowledge. Students who participate in the discovery learning process will remember longer than the conventional teaching method. This teaching method is very important in the process of teaching innovation in Vietnam when changing from a teaching method that focuses on knowledge transmission to one that focuses on developing learners' capacity. Our study proposes an exploratory teaching method for calculating the side lengths of right triangles using the Pythagoras theorem with the help of GeoGebra software. By the method of empirical investigation, we surveyed 51 students in Bien Hoa city and used descriptive statistics with the help of SPSS software, the research has shown that the discovery teaching of calculating side lengths of right triangles using Pythagoras theorem with the help of GeoGebra software is needed. However, many teachers still do not fully understand the discovery teaching method. The research results also show that there are three groups of factors affecting the way of discovery teaching. First, the effort of teachers in teaching discovery is huge. Second, the time spent on discovery teaching is relatively large. Third, the current teaching environment has not yet met the requirements of discovery teaching. The findings from the research results are important for proposing a way of discovery teaching about calculating the side lengths of right triangles using Pythagoras theorem with the help of GeoGebra software.

Caliper navigation for craniotomy planning of convexity targets

Introduction A technique to localize a radiological target on the head convexity fast and with acceptable precision is sufficient for surgeries of superficial intracranial lesions, and of help in the setting of emergency surgery, computer navigation breakdown, limited resources and education. We present a caliper technique based on fundamental geometry, with inexpensive and globally available tools (conventional CT or MRI image viewer, calculator, caliper). Methods The distances of the radiological target from two landmarks (nasion and porus acusticus externus) are assessed with an image viewer and Pythagoras’ theorem. The two distances are then marked around the landmarks onto the head of the patient with help of a caliper. The intersection defines the target. We tested the technique in a saw bone skull model and afterwards in the operating room. Convexity targets were localized with the caliper navigation technique and then with computer navigation as ground truth. Results In the saw bone model, the mean offset between the caliper navigated target and the real target was 2.9 ± 2.8 mm, 95% CI (1.6 mm; 4.2 mm). The mean offset between computer navigated target and real target was 1.6 ± 0.9 mm, 95% CI (1.2 mm; 2 mm) (ns). In 15 patients undergoing navigated cranial procedures, 100 targets were assessed in reference to computer navigation. The mean offset of the caliper navigation was 11 ± 5.2 mm, 95% CI (9.9 mm; 12 mm). Conclusion This is a low-tech approach for translation of a radiological target to the patient’s head in short time and with globally available inexpensive tools, with satisfying precision for many procedures.

An Analysis of Student Difficulties in Mathematics Learning in terms of Student Mathematical Connection Ability on Pythagoras Theorem

This research aimed to describe student difficulties in mathematics learning in terms of student mathematical connection ability on Pythagoras theorem. This research was a qualitative descriptive research with case study design. The research subjects were 18 the IX grade students, then reduced to 5 students and purposive sampling technique was used in this research. Triangulation data such as mathematical connection ability and difficulties of mathematic learning tests and interview were used for collecting the data. The data were analyzed by Miles and Hubermen techniques including three stages: reduction, presentation, and conclusion/verification. The findings of this research showed that, each respondent has different difficulties at each mathematical connection ability level; (1) The subject (very high) mathematical connection ability level did not have problem with all indicators of difficulties in mathematics learning; (2) The subject (high) mathematical connection ability level had associations or visual-motor combination; (3) The subject (medium) mathematical connection ability level had associations or visual-motor combination and difficulties in recognizing and using symbols; (4) The subject (low) mathematical connection ability level had little spatial disruption, association or visual-motor combination, and little difficulties in recognizing and using symbols; (5) The subject (very low) mathematical connection ability level had spatial disruption, association or visual-motor combination, and difficulties in recognizing and using symbols

Improving Student’s Higher-Order Thinking Skills in Solving Pythagoras Theorem Problems through Digital Learning Module

The aim of this study is to improve student’s higher-order thinking skills (HOTS) in solving Pythagoras theorem problems through digital learning module. The digital learning module involved in this study is the i-Think module (Mi-T1). This study employed the quasi experimental design with pre and post-test applied to both, control and experimental groups. The control and experimental groups consisted of the same number of Form One (aged between 12 and 13 years old) student that about 30 students each, with the control group had 14 females and 16 males, whereas the experimental group had 15 males and 15 females. Learning activities were carried out according to the teacher’s time-table and were completed in 5 weeks, approximately 10 hours per group, whereby the control group used the official text book (provided by the Ministry of Education for all students to be used in school) and the experimental group utilized Mi-T1. In addition, a survey was administered to the experimental group to measure the participants’ perceived usefulness of digital learning module. The analysis of independent sample t-test showed that the experimental group had significantly improved in their higher-order thinking skills compared to the control group. The survey data also indicated that the participants in the experimental group perceived the usefulness of the digital learning module to be equally high. Premised on these findings, the digital learning module, Mi-T1 can be used to improve students’ higher-order thinking skills in solving Pythagoras Theoremproblems.