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**Related Advancement**

- Architecture, Aviation, Chess, Cooking, Digital Technology, Drafting, Electronics, Energy, Engineering, Entrepreneurship, Game Design, Home Repairs, Metalwork, Model Design and Building, Nuclear Science, Orienteering, Personal Management, Pioneering, Programming, Robotics, Salesmanship, Surveying, Welding, and Woodwork merit badges
- Nova and Supernova awards

**Areas of Mathematics**

Mathematics is the study of numbers and their application to describing the world around us. We use numbers every day of our lives, sometimes without thinking about it. For example, when you glance at a clock, you instantly know what time it is without doing any conscious calculations.

**Arithmetic**is the study of quantity. It consists

of counting and combining numbers through addition, subtraction, division, and multiplication.**Geometry**deals with describing the shape,

size, position, and physical characteristics of lines and solids.**Statistics**is the study of collecting and analyzing data, while**probability**enables us to describe the likelihood of an event occurring. When combined, these two disciplines use knowledge from the past to try to predict what might happen in the future.

**Calculate Your Horsepower**. First find out how much you weigh in kilograms. Multiply your weight in pounds by 0.454 to get kilograms. Next, find a set of stairs. Measure the height (not the length) of the stairs from the bottom to the ending point at the top and write it down. Do this by multiplying the height of one stair by the number of stairs (it doesn’t matter how long the stairs are).

— Take a running start toward the stairs. When you step on the first step, start the timer; when both feet are on the top step, stop the timer. You may skip stairs. Now you have all the numbers needed.

— Now calculate the Power (P) with this formula: mah/t (m*9.80*h)/t, where:

m= mass (your weight) in kilograms

a= acceleration (9.80 m/sec2 is the acceleration caused by Earth’s gravity)

h= height of staircase in meters

t= time in seconds

— The number you get is in watts, which is equal to joules per second (J/s) and newton meters per second (Nm/s). If you don’t divide by time, you will calculate the energy needed to climb the stairs.

— Work = mah Power = mah/t

— Work (or energy) is measured in newton meters or joules; power is measured in joules/second or watts. Divide the number of watts by 745.6 to get the number in horsepower.

**Areas of Study** – Mathematics has two main areas of study. Though they overlap, they can be broken down into general categories.

**Bungee Jumping Rubberbands**

— If you have ever watched bungee jumpers and wondered why they don’t hit the ground, make this model to find an answer. This activity requires at least two people and works much better with a group of three to six people.

— The scenario: The Acme Daredevil Adventure Company offers the bungee jumping experience to its clientele. The company has picked a site for bungee jumping. Your task is to simulate bungee jumping using rubber bands and an action figure (doll) to determine the ultimate length, or the number of rubber bands to be used with your action figure at any given height to guarantee a safe jump. For maximum thrills, the jump must allow your action figure to come as close to the floor as possible.

— Set up the simulation. Tape a weight(s) to the doll’s back so that it is heavy enough to stretch the rubber band “bungee cord.” Tie one or two rubber bands (the unstretched size should be about 4 inches) to the doll’s feet and drop it, headfirst, from various heights. Keep raising the jump height until the head no longer hits the floor. Once you reach this height, perform three trials, measure the height of the drop each time, calculate the average, and calculate the maximum error between the average and the drop heights used to find that average. (Conduct a test drop several times to practice taking readings.) Continue adding rubber bands to see what the average drop height will be for different numbers of rubber bands. Do the experiment with at least six different quantities of rubber bands. Use a tabular chart to help you organize and record your data. (You may use Excel or create your own tables.)

Mathematics |
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