100.08 Pythagoras theorem by sliding a triangle

This paper explains step-by-step how to construct the 3D Pythagoras' theorem by geometric manipulation of the two dimensional version. In it is shown how $x+y=z$ (1D Pythagoras' theorem) transforms into $x^2+y^2=z^2$ (2D Pythagoras' theorem) via two steps: a 90-degree rotation, and a perpendicular extrusion. Similarly, the 2D Pythagoras' theorem transforms into 3D using the same steps. Octahedrons emerge naturally during this transformation process. Hence, each of the two dimensional elements has a direct three dimensional equivalent. Just like squares govern the 2D, octahedrons are the basic elements that govern the geometry of the 3D Pythagoras' theorem. As a conclusion, the geometry of the 3D Pythagoras' theorem is a natural evolution of the 1D and 2D. This interdimensional evolution begs the question -- Is there a bigger theorem at play that encompasses all three?

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Improving Mathematics Learning Outcomes Through Cooperative Learning Model Type NHT In Grade VIII A Students MTS Muhammadiyah

Formatif Jurnal Ilmiah Pendidikan MIPA ◽

10.30998/formatif.v8i1.2319 ◽

2018 ◽

Vol 8 (1) ◽

Author(s):

Muhamad Ruslan Layn

Keyword(s):

Cooperative Learning ◽

Learning Outcomes ◽

Mathematics Learning ◽

Learning Model ◽

Male Students ◽

Average Score ◽

Test Results ◽

Average Value ◽

Class Viii ◽

Pythagoras Theorem

This research is a Classroom Action Research (PTK), which aims to improve the learning outcomes of mathematics through NHT type cooperative learning model in students of class VIII A MTs. Muhammadiyah conducted collaboratively between researchers and teachers of mathematics studies. In the implementation of this research, it is done by giving group worksheet and observation sheet of student activity using NHT type cooperative learning model after giving an explanation about Pythagoras Theorem material as much as two cycles that cycle I and II. After being given group worksheets then conducted the assessment includes assessment of test results of a cycle I and cycles II and group worksheet to students that is by applying learning model of cooperative learning type NHT. The subjects of this study were students of class VIII A which amounted to 20 students consisting of 15 male students and 5 female students. Techniques of collecting data in research are this observation and test. The data obtained were then analyzed. The results of the study showed that the implementation using NHT type cooperative learning model on Pythagoras Theorem material. the ability of students in solving problems on the material above has increased. With the increase of the average value of students in the first cycle was 43.45 and increased in cycle II 83.90. Improvement of student learning outcomes to mathematics learning using NHT type cooperative learning is good. This is indicated by the average value of group learning outcomes in cycle I 60.00 or being in the medium category and the average score of the learning outcomes of the group in cycle I 82.50 or in the high category. This shows the result of increased mathematics learning after conducting cooperative learning model of NHT type

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