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2024.2.25 日曜数学会 二世@m̲2sei
3種類の立体と
3種類の穴
形(と色)の合う穴に
立体を入れる
形(と色)の違う穴には入らない
こうなる条件が気になる!
辺の長さの条件を調べる
辺の長さの条件を調べる
Ball
triangular
Pyramid
Cube
Circle
Triangle
Square
B
P C
D
T S
辺の長さの条件を調べる
B < D …… ①
P < T …… ②
C < S …… ③
B D
立体より
穴の方が大きい
T
S
P
C
各辺の長さは
穴の方が大きい
立体 穴
<
<
<
B
T
S
P
<
<
<
D < P …… ④
3T < ( 3+2)C …… ⑤
S < B …… ⑥
D
C
3(T-C)
2
C
3(T-C)
2
< C
3T < ( 3+2)C
穴 立体
B
T
S P
D
C
2C
D < 2C …… ⑦
T < 3B …… ⑧
2S < P …… ⑨
T
2 3
B
2
<
<
<
<
穴 立体
P
B
P
C
D
T
S
B < D …… ①
P < T …… ②
C < S …… ③
D < P …… ④
3T < ( 3+2)C …… ⑤
S < B …… ⑥
D < 2C …… ⑦
T < 3B …… ⑧
2S < P …… ⑨
B
P
C
D
T
S
S
T/ 3
< B < D
(2 3 - 3)T
< C < S
< P < T
D
D/ 2
2S
B < D <
P < T <
C < S <
2C
3B
B
条件をまとめる
《立体の辺の長さ》 《穴の辺の長さ》
(1+2/ 3)C
P
P/ 2
B=5.5cm
P=7.7cm
C=4.4cm
これらに合う穴を
作ることはできるか?
実践
B = 5.5cm
P = 7cm
C = 4.4cm
5.5 = B < D <
7 = P < T <
4.4 = C < S <
2C =6.16
P = 7
3B = 9.35
(1+2/ 3)C = 9.58
B = 5.5
P/ 2 = 5
5.2 < D < 6.16
7 < T < 9.35
4.4 < S < 5
D
T
S
穴の辺の長さ
立体の辺の長さ
作った
できた!
B
P
C
D
T
S
S
T/ 3
< B < D
(2 3 - 3)T
< C < S
< P < T
D
D/ 2
2S
B < D <
P < T <
C < S <
2C
3B
B
まとめ
《立体の辺の長さ》 《穴の辺の長さ》
(1+2/ 3)C
P
P/ 2
意外と簡単に作れた!!
Special Thanks
Kuma(@notori48)さん
我が子(1歳2ヶ月)
おまけ:立体同士のサイズの関係性
B
P
C
D
T
S
S
T/ 3
< B < D
(2 3 - 3)T
< C < S
< P < T
D
D/ 2
2S
<
B
P
C
<
B
P
C
D
T
S
B < D <
P < T <
C < S <
2C
3B
B
おまけ:穴同士のサイズの関係性
(1+2/ 3)C
P
P/ 2
<
< D
T
S

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