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General Princlpes
Published in Martin B., S.Z., of Industrial Hygiene, 2018
The Pythagorean theorem, c2=a2+b2, is used to describe the sides of a right triangle where c indicates the hypotenuse and a and b are the sides. In addition, the sum of the interior angles must equal 180° (α+β+γ=ϕ). Since we know that γ=90°, then: () α+β=π/2
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Published in Splinter Robert, Illustrated Encyclopedia of Applied and Engineering Physics, 2017
[computational, general] Geometric analysis of a triangle linking the lengths of the three edges with respect to the longest edge (c) as to the remaining edges (respectively a and b): c=(a2+b2). The Pythagorean theorem was defined by the Greek mathematician Pythagoras (approx. 570–490 BC).
Computer Number Systems
Published in Julio Sanchez, Maria P. Canton, Software Solutions for Engineers and Scientists, 2018
Julio Sanchez, Maria P. Canton
But not all non-integer numbers can be written as an exact ratio of two integers. The discovery of the first irrational number is usually associated with the investigation of a right triangle by the Greek mathematician Pythagoras (approximately 600 BC). Here again, irrational refers to not-a-ratio, not to “unreasonable.” The Pythagorean theorem states that in any right triangle the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides.
Recognizing the Correlation of Architectural Drawing Methods between Ancient Mathematical Books and Octagonal Timber-framed Monuments in East Asia
Published in International Journal of Architectural Heritage, 2023
The Pythagorean theorem states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the two other sides. Accordingly, the Song Yingzao Fashi’s Building Standards adopt the method of finding the hypotenuse from a right-angled triangle. Thus, the base length of the deleted triangle for drawing an octagon from a square is slightly shorter than the side length of the octagon (Liu 2014, 66). This discrepancy indicates that the theorem does not cover the equilateral octagons defined by modern mathematics [Figure 4].
Pre-service secondary mathematics teachers’ anticipation and identification of students’ thinking in the context of modelling problems
Published in International Journal of Mathematical Education in Science and Technology, 2021
Makbule Gözde Didiş Kabar, Ayhan Kürşat Erbaş
As Table 5 shows, PSMT9’s anticipations included enough detail to illustrate how students might solve the Street Parking and Bouncing Ball problems, where she provided possible details regarding how students might reason through the problems as well as various errors and difficulties that they might encounter if they were to follow her anticipated solution approach. The following excerpt illustrates anticipation with sufficient detail regarding students’ possible solution approach for the Street Park Problem. PSMT9: Students can label the length of the unknown side in the small triangle (i.e. the one with hypothenus ‘c’) as ‘a’ and then use the Pythagorean Theorem. One of the angles of the large triangle with the hypotenuseis. Both the small triangle and large triangle have right angles and corresponding equal angles. Therefore, students can use the similarity of these triangles, resulting in an equation with ‘a’ as the variable. However, they may have difficulty in solving this equation, since it includes square roots. Moreover, students can find the number of vehicles by dividing 150 by the length c. If students design includes angle parking, they can solve the problem by ignoring the fact that there will be a piece of empty area. Furthermore, as the length c becomesin the case of parallel parking, they can also investigate whether there will be cases where the length c is less thanin the case of angle parking. For this, by takingand formulating the equation, they can find the angle. Then, they can calculate the vertical width covered by the parked vehicle by using the corresponding value of this angle. [Reflection Paper 1, the Street Park Problem]