# Swimming

## The hardest to learn !

The butterfly stroke has a special place among the competitive swimming strokes. It has a reputation of being hard to learn. It requires an exact technique,strength and rhythm. It is swum on the breast, with both arms moving simultaneously, accompanied by the dolphin kick. Swimming 200 m with this stroke is hard to accomplish and is exhausting. But it can also be quite fun because of its spectacular movements.

## World Record !

Michael Phelps is the most decorated Olympian who has earned 18 gold ,2 silver,and 2 bronze medals. In 2012 he made a world record by finishing a 200 meter butterfly race in the fastest time ( 1:52:94) at the U.S nationals .Although he could not beat Chad Le Clos's time in the Olympics ( 1:52:96 ). He proved himself in the US nationals.

## A bit of brief history

The butterfly stroke evolved from the breaststroke and was considered a variant of breastroke until 1952. In 1956 butterfly was first swum as a separate competion. Since then swimmers from all over the world have been performing in this competion and earning medals. Takeshi Matsuda from Japan , Michael Phelps from USA, and Chad Le Clos from Russia are well known swimmers

## The Unlikely Match up

The olympics never had men and women compete against each other in the 200 meter butterfly stroke event. So, just out of curiosity we can predict the likely results of such an interesting match-up

## The goal of our study

The outcome of such a match up for the 200 meter butterfly stroke event can be predicted from the following data and analysis. To recognize the trends in the performances of both men and women linear regression and mathematical predictions were used. We got this data using advanced mathematical calculators.The pictures below are of the data we got in the calculator.Using the data we can now predict which gender would perform better than the other.

## The scatter plot

The blue squares represent the male competitors and the magenta X's represent the female competitors.

## Lines of best fit ( Linear Regression )

The blue line represents the trend line for the male Olympic gold medalist times and the red line represents the trend line for the female Olympic gold medalist times.

## The intersection

The intersection point of these two trend lines tells us when the men had outperformed the women in the 200 meter butterfly event. Both the trend lines are negative which means both the men and women Olympic gold medalist times are decreasing .They are getting faster over time. The blue line is the men's trend line. It is steeper so they have a faster rate of change than the red trend line for the women Olympic gold medalist times.

## The X coordinate

The X Coordinate ( independent value ) represents the years. Our X coordinate is 1322 which means the men overtook the women Olympic gold medalist times in 1322. 1322 was not a Olympic year. The next Olympic year was 1324. The men were faster than women in 1324 and will continue to be from here on out. The Olympics hadn't begun in 1324 and butterfly wasn't a part of the olympics till 1956. This means the men were faster than women from the olympics that actually included butterfly as a separate sport.

## The Y coordinate

The Y coordinate ( dependent value ) represents the Olympic gold medalist times. Our Y coordinate is 248 sec which converts to about 4 minutes and 13 sec. This is the approximate gold medalist time for both men and women if the competition had occurred in 1322. As we now know,1322 wasn't an Olympic year so the time must have been slightly lesser than 4 min and 13 seconds for both the genders. The men's Olympic gold medalist times are predicted to be faster than than the women's Olympic gold medalist times