In a right isosceles triangle with a hypotenuse of length 1, the lengths of the legs can be found using the Pythagorean theorem. Setting the length of each leg as "x," the equation becomes x² + x² = 1², simplifying to 2x² = 1. Solving for x gives x² = 1/2, leading to x = √(1/2). Rationalizing the denominator results in x = √2/2. Thus, the length of each leg in the triangle is √2/2.
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urekmazino
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For a right isosceles triangle (45-45-90) of hypotenuse 1, solve for the length of the unknown legs. Give an exact answer and rationalize the denominator in the final answer.
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes.
I have seen that this is an important subject in maths
My question is what physical applications does such a model apply to?
I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles.
In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra
Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/
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Greg tells me the feature to generate a new insight announcement is broken, so I am doing this:
https://www.physicsforums.com/insights/fixing-things-which-can-go-wrong-with-complex-numbers/