If a navigator knows that a particular star rises at the 8th direction on their star compass, what angle is this from North?
Step 1: Each direction = _____ degrees
Step 2: 8th direction = 8 × _____ = _____ degrees from North
Use the grid above to draw a simple star compass showing North and the 8th direction.
A traditional navigator plans a journey from Tahiti to Hawaii (approximately 4,000 km). Their voyaging canoe travels at an average speed of 8 km/hour when sailing.
| Journey Information | Your Calculation | Answer |
|---|---|---|
| Total distance: 4,000 km Canoe speed: 8 km/hour Calculate: Total sailing time |
_____ hours | |
| Convert to days: (Remember: 24 hours = 1 day) |
_____ days | |
| Food planning: If crew of 12 people each need 2 kg food per day, how much food needed? |
_____ kg |
Traditional navigators had to plan not just routes, but also food, water, and seasonal timing. Getting these calculations wrong could mean death at sea, so mathematical accuracy was literally a matter of survival.
Traditional navigators could detect land by reading wave patterns. When ocean swells hit an island, they create interference patterns that trained navigators could feel and interpret.
Wave Mathematics: Ocean swells travel in predictable patterns. If the main swell has a wavelength of 150 meters and travels at 15 meters per second, we can calculate wave frequency.
Wave frequency = _____ ÷ _____ = _____ Hz
This means: _____ waves pass a point every second
When waves hit an island, they reflect back. If you're 30 km from an island, and waves travel at 15 m/s, how long does it take for reflected waves to reach you?
Step 1: Convert distance to meters: 30 km = _____ meters
Step 2: Calculate time: Time = Distance ÷ Speed
Time = _____ ÷ 15 = _____ seconds = _____ minutes
Compare traditional navigation methods with modern GPS technology. Consider accuracy, reliability, and what happens when technology fails.
| Navigation Method | Accuracy | Advantages | Disadvantages |
|---|---|---|---|
| Traditional (Stars, waves, wildlife) |
±50-100 km | ||
| Modern GPS (Satellite navigation) |
±3-5 meters |
Modern ships now carry GPS, but many also train crew in traditional navigation methods. Why might this be important?
What mathematical concepts did traditional navigators use that we still use today?
How did traditional navigators solve the problem of long-distance ocean travel without modern instruments?
How could traditional navigation knowledge help improve modern navigation systems?
What did you learn today that changed your perspective on mathematics or traditional knowledge?
How does traditional Polynesian navigation demonstrate advanced mathematical thinking? Consider:
How do GPS and modern navigation systems use similar mathematical principles? What advantages and disadvantages does each approach have?