Problemas matemáticos y razonamiento · Pattern & Interval Reasoning
Visualizador de doblado y corte de cuerdas
Visualizador de problemas de doblado y corte de cuerdas y postes de valla: m·2^n + 1 segmentos
- Cálculo en cliente
- Sin registro
- Derivación en vivo
- Modo proyector
- Hoja de trabajo A4
Ventana de demostración matemática● 60 FPS
Variables de control del experimento
veces
cortes
Derivaciones y métricas en tiempo real
Total de tramos de cuerda
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Capas plegadas
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Cortes necesarios
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Fórmula de la deducción
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Derivación de fórmulas en tiempo real
Fórmula básica:
--Sustitución de valores:
--Conclusión: --
Ejemplos clásicos y análisis de errores en exámenes
Worked Problem
Problema: A rope is folded in half 4 times and cut once down the middle. How many segments unfold?
Derivación paso a paso:
- Formula: 2^n + 1. Here n=4: segments = 2⁴ + 1 = 16 + 1 = 17 segments.
Worked Problem
Problema: Clock strikes 3 times in 4 seconds. How long does it take to strike 6 times?
Derivación paso a paso:
- Look at intervals! 3 strikes have 3-1 = 2 intervals (2s/interval). 6 strikes have 5 intervals = 5 * 2 = 10 seconds.
Hoja de indagación en clase y tareas
Q1. Variant 1: Walking from 1st to 3rd floor takes 30s. At equal pace, how many more seconds to 6th floor?
Answer Key: 1st to 3rd floor is 2 flights (15s/flight). 3rd to 6th floor is 3 flights = 3 * 15 = 45 more seconds.
Q2. Variant 2: Plant trees on both sides of 100m road every 5m including both ends. How many saplings?
Answer Key: Intervals = 100/5 = 20. Single side = 20 + 1 = 21 trees. Both sides = 21 * 2 = 42 saplings.
Q3. Variant 3: Square flowerbed has 8 pots per edge including all 4 corners. How many pots altogether?
Answer Key: Prevent corner double-counting: 4 * 8 - 4 corners = 28 pots (or (8-1) * 4 = 28 pots).
Preguntas frecuentes y errores conceptuales
Why does cutting folded rope produce 2^n + 1 segments rather than 2^n?
Because U-bends stay connected! The blade slices through 2^n strands, leaving 2^n - 1 connected loops plus 2 loose ends, summing to 2^n + 1.
If a folded rope is cut with 2 blades (trisection), how many segments form?
Universal formula: Segments = m * 2^n + 1. Each additional blade adds 2^n pieces, so 2 blades produce 2*2^n + 1.
How to cleanly distinguish the 3 fencepost tree planting cases without confusion?
1) Both ends planted: Trees = Gaps + 1. 2) One end planted (or closed circle): Trees = Gaps. 3) Neither end planted: Trees = Gaps - 1.
In square army formations, how are edge counts and outer perimeter related?
Perimeter = (Edge - 1) * 4. Expanding outward by one ring adds 8 people (4 sides + 4 corners).