Ragnarok, the legendary end of the world in Norse mythology, is a time when giants, monsters, and gods clash in a battle for the future. The gods seemed to have the upper hand until the formidable serpent, Jörmungandr, emerged. This colossal creature swallowed Valhalla, stretched across the land, and formed a continuous body with no discernible head or tail.
As Jörmungandr began to digest Valhalla, a weary Odin realized he had just enough strength left for one last strike. He proposed a plan: if his lightning bolt could be amplified by the legendary hammer, Mjölnir, it might penetrate the serpent’s massive form. The task was to run with super-speed along the serpent’s body, holding the hammer high so that Odin could strike it with lightning, splitting Jörmungandr open at that point. The challenge was to continue running along its body until every part was destroyed, avoiding any previously blasted sections to prevent falling into the void.
To successfully destroy the serpent, one must leave no part un-zapped, as any untouched portion would regenerate, exhausting Odin’s last power and dooming Valhalla. The key to solving this problem lies in simplification, focusing on intersections and the stretches of the serpent between them, known in graph theory as nodes and edges.
Edges represent the paths to travel, while nodes are the decision points connecting these paths. This simplification transforms the problem into a mathematical object known as a graph or network. The goal is to find an Eulerian path, a route that traces every edge exactly once.
To understand the Eulerian path, consider a single node. During the run, you enter and exit this node, covering two edges. If you enter again, you must exit again, requiring another pair of edges. Thus, every node must have an even number of edges, except for the start and end points, where you can exit without entering or vice versa.
Examining the network formed by the serpent reveals that every node has an even number of edges, except two. These two nodes must be the start and end of the route. Any connected network with exactly two nodes having an odd number of edges will contain an Eulerian path. If no nodes have an odd number of edges, the path starts and ends at the same spot.
Returning to the full graph, the journey begins by addressing a specific edge. From there, one can zig-zag across the serpent, reaching the end. This systematic approach is just one solution; knowing where to start and end allows for discovering many other paths.
With Mjölnir held high at the perfect moment, Odin sends a world-saving surge of lightning. You run with unparalleled speed, determined to ensure the might of the Norse gods prevails. If such a feat can be accomplished, surely nothing could stand in their way. And if another threat were to arise, that would be a tale for another day.
Using a large sheet of paper, draw a simplified version of Jörmungandr as a graph with nodes and edges. Your task is to find an Eulerian path that covers every edge exactly once. Work in pairs to solve the puzzle, and then compare your solutions with your classmates.
In groups, create a short skit or digital animation that retells the story of Ragnarok and Odin’s final stand using the concepts of graph theory. Highlight the importance of finding the Eulerian path in your narrative. Present your skit or animation to the class.
Research and present a real-world application of graph theory, such as in computer networks, urban planning, or social networks. Create a visual presentation or infographic that explains how the Eulerian path concept is used in your chosen application.
Participate in a quiz that combines questions about Norse mythology and graph theory. Prepare by reviewing key concepts from the article and related class materials. The quiz can be conducted using an online platform or as a live classroom activity.
Write a short story or comic that involves a mythical creature or scenario where graph theory plays a crucial role in solving a problem. Be creative and incorporate elements from both mythology and mathematics. Share your story or comic with the class.
Ragnarok – The prophesied end of the world in Norse mythology, characterized by a great battle and the death of many gods. – In mathematics, we can think of Ragnarok as a metaphor for the end of a complex problem that requires a significant transformation to solve.
Valhalla – A majestic hall in Norse mythology where warriors who died in battle are received by Odin. – In graph theory, one might consider Valhalla as the ultimate destination for nodes that have reached their final state in a network.
Mjölnir – The mythical hammer of Thor, capable of leveling mountains and returning to his hand after being thrown. – Just as Mjölnir can break obstacles, a well-constructed graph can break down complex data into manageable parts.
Odin – The chief god in Norse mythology, associated with wisdom, healing, and knowledge. – In mathematics, we often seek the wisdom of Odin when trying to understand complex theories and concepts.
Jörmungandr – The Midgard Serpent in Norse mythology, a giant sea serpent that encircles the Earth. – In a network graph, Jörmungandr can symbolize the cyclical nature of certain functions that loop back to their starting point.
Graph – A mathematical representation of a set of objects where some pairs of the objects are connected by links. – The graph of a function can visually demonstrate the relationship between variables in a mathematical equation.
Nodes – The individual points in a graph where lines or edges meet. – In a social network, each person can be represented as a node, illustrating their connections to others.
Edges – The connections between nodes in a graph that represent relationships or pathways. – In a transportation network, edges can represent the roads that connect different cities.
Eulerian – Referring to a path or circuit in a graph that visits every edge exactly once. – Solving an Eulerian path problem can be as challenging as navigating the complexities of Norse mythology.
Network – A collection of nodes and edges that represent relationships or interactions within a system. – Understanding a network’s structure is crucial for analyzing data flow in mathematical models.
