When a shooting star crashes to Earth, it brings with it a terrifying entity: a blob that defies all attempts to stop it. This amorphous creature creeps and leaps, gliding effortlessly across the landscape. Conventional weapons, fire, and even extreme temperatures are futile against its relentless advance. Astonishingly, the blob doubles in size every hour, posing an existential threat to the planet.
Despite its formidable nature, the blob has a singular vulnerability. After each hour of growth, it pauses to rest, flattening into a triangular shape for a few minutes before resuming its destructive path. This brief period offers a critical window of opportunity to intervene using a satellite-mounted nano-fission ray capable of slicing through the blob.
When active, the blob heals almost instantly. However, a breakthrough occurs when the sleeping blob is divided into two triangles. The acute triangle, with all angles less than 90 degrees, remains inert and never reactivates. In contrast, the obtuse triangle, characterized by an angle greater than 90 degrees, awakens and continues to grow. Further experiments reveal that only acute triangles remain dormant, while other shapes, including right triangles, do not.
With the blob currently resting in an obtuse triangle form, there is a limited timeframe to act. You can make seven precise cuts while the satellite is overhead. If any part of the blob that can awaken remains, it will consume the entire world before the satellite completes its orbit and returns.
Initially, it seems impossible to avoid creating obtuse or right angles with each cut. However, inspiration can be drawn from an unlikely source: pizza. By envisioning the blob as a pizza, one can transform it from a circular shape into an octagon, where each slice forms an acute triangle. This concept applies to various polygons, including heptagons, hexagons, and pentagons.
By trimming the sharp corners of the blob’s obtuse triangle, a pentagon is formed. This shape can be divided into five acute triangles using the seven available cuts, rendering the blob completely inert. The planet is saved from impending doom!
With the immediate threat neutralized, the challenge remains of dealing with the giant, nearly indestructible acute triangles left behind. While the world is safe for now, the mystery of these triangles endures, prompting further exploration and understanding.
Using graph paper, simulate the blob’s growth by doubling its size every hour. Start with a small shape and draw its expansion over several hours. This will help you visualize the blob’s relentless growth and understand the urgency of stopping it.
Create a set of paper triangles, including acute, obtuse, and right triangles. Practice identifying each type and experiment with cutting obtuse triangles into smaller acute triangles. This hands-on activity will reinforce your understanding of triangle properties and the blob’s vulnerability.
Design a board game where you must strategically place seven cuts on a blob-shaped board to divide it into acute triangles. Use tokens or markers to represent the cuts and challenge your classmates to see who can save the planet the fastest.
Draw a large circle on paper and divide it into different polygon shapes like pentagons, hexagons, and octagons. Practice cutting these shapes into acute triangles, just like slicing a pizza. This will help you understand how to apply the pizza analogy to the blob’s shape.
Write a short story from the perspective of a scientist working to stop the blob. Describe the challenges faced, the discovery of the blob’s weakness, and the final plan to save the planet. This creative activity will help you internalize the concepts while practicing your writing skills.
Blob – A shape that is irregular and does not have straight edges or corners. – The artist used a blob of paint to create a unique shape on the canvas.
Triangle – A polygon with three sides and three angles. – In math class, we learned that a triangle can be classified as equilateral, isosceles, or scalene.
Acute – An angle that measures less than 90 degrees. – The corner of the slice of pizza formed an acute angle.
Obtuse – An angle that measures more than 90 degrees but less than 180 degrees. – The obtuse angle in the room made it feel more spacious.
Polygon – A closed figure with three or more straight sides. – A square and a triangle are both examples of polygons.
Heptagon – A polygon with seven sides and seven angles. – The heptagon has more sides than a hexagon but fewer than an octagon.
Hexagon – A polygon with six sides and six angles. – The honeycomb is made up of many hexagons that fit together perfectly.
Pentagon – A polygon with five sides and five angles. – The shape of the U.S. Department of Defense building is a pentagon.
Cuts – To divide something into parts or sections, often with a straight line. – The teacher showed us how to make straight cuts to create different shapes.
Angles – The space between two intersecting lines or surfaces measured in degrees. – We learned how to measure angles using a protractor in our geometry lesson.
