Paper cut picture: Do not stand at my grave and weep

Sometimes I make Kirie (cutting peper picture). I gave most of them to some friends. This is one of the recent my kirie. I thank Claudia for giving me a permission to put my Kirie's picture in my blog.

I translated a poem, "Sen no Kaze ni natte" (Original English "Do not stand at my grave and weep") to German from Japanese. Why did I translate it based on non-original poem? Hum, I thought I could sing it since Japanese poem has a song. But, it is difficult, of course.

---
Tausend Winde (Stehe nicht vor meinem Grab und weine)
Englisch Autor: Unbekannte (oder Mary Elizabeth Frye)
Japanische Übersetzen: 新井満 (Arai Man)
Deutsche Übersetzen: Hitoshi und Leo

Stehe nicht vor meinem Grab und weine.
Ich bin nicht dort, ich schlafe nicht.
Ich bin tausend Winde, die im Himmel wehen.

Ich bin der gänzende Diamant auf dem Schnee.
Ich bin der Sonnenstrahl auf reifem Getreide.
Am Morgen werde ich ein friedlicher Vogel
der Dich aufweckt, im kreisenden Flug.
In der Nacht werde ich die sanften Sterne.

Stehe nicht vor meinem Grab und weine.
Ich bin nicht dort, ich schlafe nicht.
Ich bin tausend Winde, die im Himmel wehen.
Ich bin überall, wo du bist.
--

Comments

Why A^{T}A is invertible? (2) Linear Algebra

Why A^{T}A has the inverse Let me explain why A^{T}A has the inverse, if the columns of A are independent. First, if a matrix is n by n, and all the columns are independent, then this is a square full rank matrix. Therefore, there is the inverse. So, the problem is when A is a m by n, rectangle matrix. Strang's explanation is based on null space. Null space and column space are the fundamental of the linear algebra. This explanation is simple and clear. However, when I was a University student, I did not recall the explanation of the null space in my linear algebra class. Maybe I was careless. I regret that... Explanation based on null space This explanation is based on Strang's book. Column space and null space are the main characters. Let's start with this explanation. Assume x where x is in the null space of A . The matrices ( A^{T} A ) and A share the null space as the following: This means, if x is in the null space of A , x is also in the n...

Gauss's quote for positive, negative, and imaginary number

Recently I watched the following great videos about imaginary numbers by Welch Labs. https://youtu.be/T647CGsuOVU?list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF I like this article about naming of math by Kalid Azad. https://betterexplained.com/articles/learning-tip-idea-name/ Both articles mentioned about Gauss, who suggested to use other names of positive, negative, and imaginary numbers. Gauss wrote these names are wrong and that is one of the reason people didn't get why negative times negative is positive, or, pure positive imaginary times pure positive imaginary is negative real number. I made a few videos about explaining why -1 * -1 = +1, too. Explanation: why -1 * -1 = +1 by pattern https://youtu.be/uD7JRdAzKP8 Explanation: why -1 * -1 = +1 by climbing a mountain https://youtu.be/uD7JRdAzKP8 But actually Gauss's insight is much powerful. The original is in the Gauß, Werke, Bd. 2, S. 178 . Hätte man +1, -1, √-1) nicht positiv, negative, imaginäre (oder gar um...

Why parallelogram area is |ad-bc|?

Here is my question. The area of parallelogram is the difference of these two rectangles (red rectangle - blue rectangle). This is not intuitive for me. If you also think it is not so intuitive, you might interested in my slides. I try to explain this for hight school students. Slides: A bit intuitive (for me) explanation of area of parallelogram (to my site, external link) .

Lx=d: SundayResearch

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