👨🏼‍✈️ 🥊 🔹 Wie man einen Weihnachtsbaum macht, wenn man Mathematiker # 2 ist 🐑 🏯 💇

Fortsetzung des gestrigen Artikels über fYolka unten.

Basisfunktionen

Trapez

$y = \ left | x-4 \ right | + \ left | x + 2 \ right | -5.5$

Hier wird der Modul der Zahl zweimal angewendet, wobei die Konstanten unter dem Modul geändert und subtrahiert werden. Wir können die Länge des Segments mit einem konstanten Wert y und dem Wert von y selbst auf diesem Segment anpassen. Diese Funktion wird später für Drifts und Eimer nützlich sein.

Alternative Ellipse

$\ sqrt {\ left (x-1 \ right) ^ {2} +1.9 \ left (y-2 \ right) ^ {2}} - 1.3 = 0$

Alternative Ellipsennotation. Die Konstanten in den Klammern sind für die Koordinaten des Mittelpunkts der Ellipse verantwortlich, die Konstanten vor den Klammern sind für das Kompressionsverhältnis entlang der Achsen, die Zahl hinter der Wurzel ist der Radius.

Ellipse um zwei Punkte

$\ sqrt {\ left (x-1 \ right) ^ {2} + \ left (y-2 \ right) ^ {2}} + \ sqrt {\ left (x-0.1 \ right) ^ {2} + \ links (y + 1 \ rechts) ^ {2}} - 3,3 = 0$

, - , (A B ) . .

, .

$\ max \ left (\ left | x \ right | -1, \ left | y \ right | -1 \ right) \ le0$

- :

$\ max \ left (\ left | x \ right |, \ left | y \ right | \ right) \ le1$

-

$s_ {1} = \ sqrt {\ left (x-10 \ right) ^ {2} +1.1 \ left (y-3.85 \ right) ^ {2}} - 0.55$ $s_ {2} = \ sqrt {\ left (x-10 \ right) ^ {2} +1.1 \ left (y-2.7 \ right) ^ {2}} - 0.85$ $s_ {3} = \ sqrt {\ left (x-10 \ right) ^ {2} +1.2 \ left (y-1.05 \ right) ^ {2}} - 1.15$

- min .

$\ min \ left (s_ {1}, \ s_ {2}, s_ {3} \ right) \ le0$

!

-

$- \ left | x-1 \ right | - \ left | x + 1 \ right | -y \ ge0$

- ,

$2-1.9\left|x-0.3\right|-1.9\left|x+0.3\right|-y\ge0$

, - 2 , - .

-

, .

$x=\frac{\left(\left|y\right|+y\right)}{2}$

$x=\frac{100\left(\left|y\right|-y\right)}{2}$

$x=\left(\frac{\left(\left|y\right|+y\right)}{2}+\frac{100\left(\left|y\right|-y\right)}{2}\right)$

$2-1.9\left|x-0.3\right|-1.9\left|x+0.3\right|-\left(\frac{\left(\left|y\right|+y\right)}{2}+\frac{100\left(\left|y\right|-y\right)}{2}\right)\ge0$

-

$2-1.9\left|x-9.7\right|-1.9\left|x-10.3\right|-\left(\frac{\left(\left|y-4\right|+y-4\right)}{2}+\frac{100\left(\left|y-4\right|-y+4\right)}{2}\right)\ge0$

$s_{4}=2-1.9\left|x-9.7\right|-1.9\left|x-10.3\right|-\left(\frac{\left(\left|y-4\right|+y-4\right)}{2}+\frac{100\left(\left|y-4\right|-y+4\right)}{2}\right)$ $\min\left(s_{1},\ s_{2},s_{3},-s_{4}\right)\le0$

s₄ , >0, <0, .

-

- x = 10, , , .

$h_{1}=\sqrt{\left(\left|x-10\right|\ -\ 0.8\right)^{2}+\left(y-2.7\right)^{2}}+\sqrt{\left(\left|x-10\right|\ -\ 2.8\right)^{2}+\left(y-2.5\right)^{2}}-2.015\\h_1\le0$

, = 10, = 2.55

$h_{2}=\sqrt{\left(\left|x-10\right|\ -\ 1.9\right)^{2}+\left(y-2.55\right)^{2}}+\sqrt{\left(\left|x-10\right|\ -\ 2.3\right)^{2}+\left(\left|y-2.55\right|-0.3\right)^{2}}-0.51\\h_2\le0$

$\min\left(s_{1},\ s_{2},s_{3},-s_{4},h_{1},h_{2}\right)\le0$

- 2

$100\left(\left|x-10\right|-0.2\right)^{2}+100\left(y-3.95\right)^{2}\le1$

-

$\left(300\left(\left|x-10\right|-0.03-0.-\left(y-3.6\right)\right)^{2}+3000\left(y-3.6\right)^{2}\right)\le1$

desmos

s_{1}=\sqrt{\left(x-10\right)^{2}+1.1\left(y-2.7\right)^{2}}-0.85

s_{2}=\sqrt{\left(x-10\right)^{2}+1.2\left(y-1.05\right)^{2}}-1.15

s_{3}=\sqrt{\left(x-10\right)^{2}+1.1\left(y-3.85\right)^{2}}-0.55

s_{4}=2-1.9\left|x-9.7\right|-1.9\left|x-10.3\right|-\left(\frac{\left(\left|y-4\right|+y-4\right)}{2}+\frac{100\left(\left|y-4\right|-y+4\right)}{2}\right)

h_{1}=\sqrt{\left(\left|x-10\right|\ -\ 0.8\right)^{2}+\left(y-2.7\right)^{2}}+\sqrt{\left(\left|x-10\right|\ -\ 2.8\right)^{2}+\left(y-2.5\right)^{2}}-2.015

h_{2}=\sqrt{\left(\left|x-10\right|\ -\ 1.9\right)^{2}+\left(y-2.55\right)^{2}}+\sqrt{\left(\left|x-10\right|\ -\ 2.3\right)^{2}+\left(\left|y-2.55\right|-0.3\right)^{2}}-0.51

\min\left(s_{1},\ s_{2},s_{3},-s_{4},h_{1},h_{2}\right)\le0

100\left(\left|x-10\right|-0.2\right)^{2}+100\left(y-3.95\right)^{2}\le1

\left(300\left(\left|x-10\right|-0.03-0.-\left(y-3.6\right)\right)^{2}+3000\left(y-3.6\right)^{2}\right)\le1

- . .

$d_{1}=-\left|x+7\right|-\left|x-14\right|+22\\d_{2}=\left|x+2.7\right|+\left|x-2.7\right|-6.35\\d_{3}=\left|x-9\right|+\left|x-11\right|-2.8$

$d=d_{1}+\left|d_{1}\right|+d_{2}-\left|d_{2}\right|+d_{3}-\left|d_{3}\right|$

$0.3d\left|\sin\left(13x\right)\right|$

d_{1}=-\left|x+7\right|-\left|x-14\right|+22

d_{2}=\left|x+2.7\right|+\left|x-2.7\right|-6.35

d_{3}=\left|x-9\right|+\left|x-11\right|-2.8

d=d_{1}+\left|d_{1}\right|+d_{2}-\left|d_{2}\right|+d_{3}-\left|d_{3}\right|

0.3d\left|\sin\left(13x\right)\right|

. - " ", , , x .

$\sqrt{\left|x\right|}+\sqrt{\left|y\right|}-0.45\le0$

mod,

$\left|\operatorname{mod}\left(x,2\right)-1\right|$

$f_{1}=\sqrt{\left|\operatorname{mod}\left(x,2\right)-1\right|}+\sqrt{\left|\operatorname{mod}\left(y,2\right)-1\right|}-0.45\\f_1\le0$

, .

$f_{2}=2xx+\left(y-6\right)^{2}-40\\f_{3}=2\left(x-10\right)^{2}+\left(y-2.5\right)^{2}-10\\f_2\le0\\f_3\le0$

$\min\left(-f_{1},f_{2},f_{3}\right)\ge0$

f_{1}=\sqrt{\left|\operatorname{mod}\left(x,2\right)-1\right|}+\sqrt{\left|\operatorname{mod}\left(y,2\right)-1\right|}-0.45

f_{2}=2xx+\left(y-6\right)^{2}-40

f_{3}=2\left(x-10\right)^{2}+\left(y-2.5\right)^{2}-10

\min\left(-f_{1},f_{2},f_{3}\right)\ge0

- . , |x| .

$j_{1}=\left|0.9\left|\left|x\right|-2.1\right|\right|-\left(y-1\right)-0.2\\j_1\le0$

$j_{2}=\left|\left|x\right|-2.1\right|^{2}-\left(y-1\right)^{2}-0.05\\j_2\ge0$

$j_{3}=0.2\left|\left|x\right|-2.1\right|^{2}+0.2\left(y-1\right)^{2}-0.1\\j_3\le0$

$j_{4}=\left(0.5\left|\left|x\right|-2.1\right|\right)^{2}+\left(y-1\right)^{2}-0.02\\j_4\le0$

:

$j_1j_4\le0$

$\max\left(j_{1}j_{4},\ -j_{2},\ j_{3}\right)\le0$

j_{1}=\left|0.9\left|\left|x\right|-2.1\right|\right|-\left(y-1\right)-0.2

j_{2}=\left|\left|x\right|-2.1\right|^{2}-\left(y-1\right)^{2}-0.05

j_{3}=0.2\left|\left|x\right|-2.1\right|^{2}+0.2\left(y-1\right)^{2}-0.1

j_{4}=\left(0.5\left|\left|x\right|-2.1\right|\right)^{2}+\left(y-1\right)^{2}-0.02

\max\left(j_{1}j_{4},\ -j_{2},\ j_{3}\right)\le0

, , .

$x_{1}=x\\y_{1}=y$

2021 MMXXI,

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t2,

$t_{2}=\max\left(\left|\left|x_{1}\right|-1\right|,\left|y_{1}-0.89\right|\right)-0.95\\t_{2}\le0$

"",

$\max\left(\left|1.2\left|x_{1}\right|-1.2\right|,\left|y_{1}-0.9\right|\right)-1\ge0$

V-

$\min\left(\left|2\left|x_{1}\right|-2\right|-y_{1},-\left|2\left|x_{1}\right|-2\right|+y_{1}+0.2,-t_{2}\right)\ge0$

$\max\left(\min\left(-t_{2},\max\left(\left|1.2\left|x_{1}\right|-1.2\right|,\left|y_{1}-0.9\right|\right)-1\right),\min\left(\left|2\left|x_{1}\right|-2\right|-y_{1},-\left|2\left|x_{1}\right|-2\right|+y_{1}+0.2,-t_{2}\right)\right)\ge0$

""

$\max\left(\left|\left|x_{1}\right|-1.05\right|,\left|y_{1}-0.9\right|\right)-1\le0$

$\min\left(\left|\left|x_{1}\right|-1.05\right|-\left|y_{1}-0.9\right|,\ -\left|\left|x_{1}\right|-1.05\right|+\left|y_{1}-0.9\right|+0.15\right)\ge0$

$\ max \ left (- \ min \ left (\ left | \ left | x_ {1} \ right | -1.05 \ right | - \ left | y_ {1} -0.9 \ right |, \ - \ left | \ left | x_ {1} \ rechts | -1,05 \ rechts | + \ links | y_ {1} -0,9 \ rechts | +0,15 \ rechts), \ max \ links (\ links | \ links | x_ {1} \ rechts | -1,05 \ rechts |, \ links | y_ {1} -0,9 \ rechts | \ rechts) -1 \ rechts) \ le0$

4.1 ,

$\ max \ left (- \ min \ left (\ left | \ left | x_ {1} -4.1 \ right | -1.05 \ right | - \ left | y_ {1} -0.9 \ right |, \ - \ left | \ left | x_ {1} -4.1 \ right | -1.05 \ right | + \ left | y_ {1} -0.9 \ right | +0.15 \ right), \ max \ left (\ left | \ left | x_ {1 } -4.1 \ rechts | -1.05 \ rechts |, \ links | y_ {1} -0.9 \ rechts | \ rechts) -1 \ rechts) \ le0$

"I"

, "I"

$\ max \ left (\ left | x_ {1} -6.4 \ right | -0.06, \ left | y_ {1} -0.9 \ right | -01 \ right) \ le0$

t_{2}=\max\left(\left|\left|x_{1}\right|-1\right|,\left|y_{1}-0.89\right|\right)-0.95

\max\left(\min\left(-t_{2},\max\left(\left|1.2\left|x_{1}\right|-1.2\right|,\left|y_{1}-0.9\right|\right)-1\right),\min\left(\left|2\left|x_{1}\right|-2\right|-y_{1},-\left|2\left|x_{1}\right|-2\right|+y_{1}+0.2,-t_{2}\right)\right)\ge0

\max\left(-\min\left(\left|\left|x_{1}-4.1\right|-1.05\right|-\left|y_{1}-0.9\right|,\ -\left|\left|x_{1}-4.1\right|-1.05\right|+\left|y_{1}-0.9\right|+0.15\right),\max\left(\left|\left|x_{1}-4.1\right|-1.05\right|,\left|y_{1}-0.9\right|\right)-1\right)\le0

$x_ {1} = \ left (x \ -8 \ right) \ cdot1.3 \\ y_ {1} = \ left (y-9.3 \ right) \ cdot1.3$

, - , , , sin(x), x∈(-5, 5). .

$min = \ frac {f + g} {2} - \ left | \ frac {fg} {2} \ right | \\ max = \ frac {f + g} {2} + \ left | \ frac {fg} {2} \ right |$

Daher ist die Verwendung der Min- und Max-Funktionen in Zahlenformeln bei dieser Aufgabe zulässig.

Wie man einen Weihnachtsbaum macht, wenn man Mathematiker # 2 ist

Basisfunktionen

Trapez

Alternative Ellipse

Ellipse um zwei Punkte

-

!

-

- ,

-

-

-

- 2

-

desmos

:

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