Difference between revisions of "MR 05 Loesung"
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Man sieht sofort, dass die beiden äußeren Kerzen den Abstand <math>x - y</math> und die beiden innern Kerzen den Abstand <math>2y</math> haben. Des weiteren fällt auf, dass (wegen r=1) <math>x^2 + y^2 = 1^2</math> ist. | Man sieht sofort, dass die beiden äußeren Kerzen den Abstand <math>x - y</math> und die beiden innern Kerzen den Abstand <math>2y</math> haben. Des weiteren fällt auf, dass (wegen r=1) <math>x^2 + y^2 = 1^2</math> ist. | ||
| − | Die beiden inneren Kerzen und die äußeren mussen laut Aufgabenstellung den gleichen Abstand haben. | + | Die beiden inneren Kerzen und die äußeren mussen laut Aufgabenstellung den gleichen Abstand ''a'' haben. |
| + | |||
| + | <math>a = 2y</math> | ||
| + | |||
| + | <math>a = x - y</math> | ||
<math>2y = x - y</math> | <math>2y = x - y</math> | ||
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<math>3y = \sqrt{1 - y^2}</math> | <math>3y = \sqrt{1 - y^2}</math> | ||
| + | |||
| + | <math>9y^2 = 1 - y^2</math> | ||
| + | |||
| + | <math>10y^2 = 1</math> | ||
| + | |||
| + | <math>y = \sqrt{ 1 \over 10 }</math> | ||
| + | |||
| + | <math>a = 2y = 2 \sqrt{ 1 \over 10 }</math> | ||
Revision as of 18:22, 10 January 2018
Advendkranz drehen
So sieht der Kranz mathematisch aus. Das rote sind die Kerzen. Die jeweiligen Dreiecke sind deckungsgleich und die blauen und orangenen Linien sind gleich lang.
Man sieht sofort, dass die beiden äußeren Kerzen den Abstand Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x - y} und die beiden innern Kerzen den Abstand Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2y} haben. Des weiteren fällt auf, dass (wegen r=1) Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x^2 + y^2 = 1^2} ist.
Die beiden inneren Kerzen und die äußeren mussen laut Aufgabenstellung den gleichen Abstand a haben.
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = 2y}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = x - y}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 2y = x - y}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3y = x}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 3y = \sqrt{1 - y^2}}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 9y^2 = 1 - y^2}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 10y^2 = 1}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = \sqrt{ 1 \over 10 }}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a = 2y = 2 \sqrt{ 1 \over 10 }}