In the absence of inns, paths, signs and other navigational cues, determining the intended course and finding one’s position could be an intractable problem. Trigonometry is a branch of mathematics that is used in the study and use of angles and length in relation to various points on a plane (Linton, 2004). The European sailors in the 15th and 16th centuries undertook navigation to various continents in the world as they were out to accomplish various missions. Trigonometry was an integral part of their experience.
Eric (1998) outlines that one of the most difficult experiences that they went through was uncertainty because of the lack of landmarks or signs in the sea. The European sailing experience was a great adventure in the medieval craft of pilotage as it acted as a big step in the application of trigonometry to improve the qualitative art of navigation. Trigonometry was very crucial in their adventures as it provided some spatial and geographical thoughts that contributed to the success of their adventures.
Whereas most of the medieval pilots had relied on their experience and intensive personal familiarity with the routes that they sailed in order to trace their way. There was no such empirical frame for the modern explorer for reference and guidance in the open and strange waters without landmarks. For this challenge, he had to adopt modern techniques like the charts to arrive at the intended landfall. This device assisted the pilots to calculate the campus headings and the distances between two places (Linton, 2004). All these calculations were based on estimations.
Besides keeping track of the distance travelled and the heading direction, the sailors had to do their best to keep off any distractions and travel in a straight line. Maintaining of the celestial points as reference in order not to miss the intended course because of wind and storms was very essential. By the middle ages, Mediterranean sailors acquired some instruments like the magnetic campuses to help them keep their course in case they strayed (Eric, 1998). This was later enhanced by the ‘portolan charts’ from Italy.
According to (Linton, 2004), these charts facilitated major advancements in the navigation industry. This assisted the sailors to plot optimal dead reckoning courses with greater confidence and accuracy. This was possible through the determination of the distance between the point of origin and destination. Using a divider, the heading campus was easily determined. However, these charts gave the sailors confidence and control in plotting between ports in North Africa, Southern Europe, and the Levant. They provided less convenience in travels that were outside Mediterranean.
In order to supplement their traditional navigational techniques, the Portuguese developed new technology for confirming the locations of the ship in the sea (Dampier, 1997). They made use of astronomical observation. They used stars as a way of confirming the position of the observer on the earth. This had been possible before only with recourse to earthbound reference points and rough estimation of the distance travelled by use of the traditional method of dead reckoning.
Dampier (1997) explains that in the last half of the fifteenth century, the Portuguese sailors learned how to use simple versions of ancient tools used by astronomers. These tools were the astrolabe and the quadrant. These tools were designed to help astronomers with a number of complicated calculations. These tools had stereographic mathematical projections that required mastery of mathematical functions for effective use.
Dampier (1997) outlines that in the 16th century, there was a lot interaction between the Europeans and the Arabs. This interaction made the Europeans adopt the use of the astronomical instruments that the Arabs used to navigate with through the Indian Ocean. These instruments were used to measure the altitude. The distance could be determined after a few trigonometric calculations. The scales on these quadrants could assist in obtaining the angular elevation of points in relation to the rays of the sun. The accuracy of the measurements obtained by these instruments was affected by the stability of the instruments in case there were high winds in the sea.
In the 16th century, the European navigators learned how to think and measure their location on the earth in terms of angles. This was a logical move towards the development of the charts as the designers logically put it into account while drawing their charts. The earlier charts were drawn using the rough estimates of the direct distances between objects.
Latitude figures were taken from astronomical observations was far more precise, and they replaced the traditional use of linear distances (Eric, 1998). Portuguese cartographers took this into consideration, and they produced charts that had the scale of latitude in the early 16th century. These radical innovations made the sailors perceive their work more geometrically. This is by including the angular distance as well.
For the Spanish and Portuguese traders, sailing did not present so many problems as they had established their equatorial trade links to West Indies and New World. The Northern European explorers faced difficult situations. What seemed like an ultimate innovation that assisted in the navigation industry was an invention by English Mathematician Edward Wright (Linton, 2004). He invented a mathematical solution known as Mercator whose scale was used to plot accurate courses at sea.
In conclusion, the cultural orientations of the European travelers that included interaction and exchange of ideas led to the discovery of navigational methods that assisted the sailors. All these methods that were used integrated use of trigonometric models and mathematical solutions in the determination of distance and direction. In the 15th and 16th centuries, the navigation of the European sailor was made easy with the advancing technology. This also led to evolution and advancement of trigonometry.
- Dampier, W. (1997). A Voyage around the World. London. Gutenberg. Eric, W. (1998). Early Application of Trigonometric Formulas. NY. Wolfram press.
- Linton, M. C. (2004). Mathematical Astronomy History. Cambridge. Cambridge University Press.