Mathematical Patterns and Relations

Topics: Mathematics, Probability theory, Statistics Pages: 11 (3656 words) Published: April 20, 2013
Task 1: Big Foot
Part 1
After viewing some background information on the yowie (a short video and newspaper article), we were given the foot length of the yowie (43cm) and asked to find its height from this measurement. We were asked to collect a series of measurements of our body proportions. After some discussion about not getting precise enough approximation for some body proportions, specifically the a/b/c finger, we decided to only include foot length, height and arm span as we thought that this was the essence of the our initial question. Based on our initial foot measurements we agreed that for our estimation of the yowie’s height we would double Tamara’s height as her foot measurement doubled was the closet to the yowie’s (157x2=314) making our height estimate to be 314cm. Our body proportion can be seen in table 1. Name and Scale Factor *| Yowie’s height estimate (nearest cm)| Kate’s Scale Factor (6.75x43)| 290|

Maybelline’s Scale Factor (6.65x43)| 286|
Ashleigh’s Scale Factor (6.70x43)| 288|
Tamara’s Scale Factor (7.48x43)| 322|
Mean Scale Factor(6.895x43)| 296|
Table 1 - Body Measurements Used Table 2 - Scale Factor Height Estimate Name| Foot Length (cm)| Height^(cm)| Arm Span(cm)|

Kate (Me)| 24| 162| 167|
Maybelline| 23| 153| 156|
Ashleigh| 24| 161| 154|
Tamara| 21| 157| 150|
Yowie | 43| 296| |
^Note. Yowie Height is the mean scale factor estimate

*Note. All calculations made with a calculator

We calculated our scale factors (SF) by dividing our height from our foot length (e.g., Maybelline’s SF 153/23 = 6.65 2dp)* which gave us a SF of 6.75 for me, 6.70 for Ashleigh and 7.48 for Tamara. Table 2 shows the yowie’s height based on our SFs. Next we decided to find the mean of our SFs and to work out the yowie’s height (6.75+6.65+6.70+7.48/4=6.895)*, which is also indicated in Table 2. We came to the conclusion that the yowie was 296cm tall as we deemed that the mean scale factor would be a better indicator. However, it should be noted that all our yowie height calculations and the initial estimates indicated that the yowie is approximately 300cm tall. Part 2

Table 3 Percentage of Arm Span to Height
Arm Span to Height (nearest cm)| Precent (2dp)|
Kate (167/162x100)| 103.09|
Maybelline (156/153x100)| 101.96|
Ashleigh (154/161x100)| 95.65|
Tamara (150/157x100)| 95.54|
There are several ways to extend the investigation. Our group decided to compare the percentage difference between our Arm span and height, to test the Da Vinci Vitruvian Man theory (Drexel University, 2013), that arm span and height are equal. This is shown in table 3. It seems to show that arm span and height are very similar measurements, with all of us within 5% of our height. More ways to extend the investigation include questions like: What if you were archaeologist and discovered a mass human grave, would you be able to group the together correct bones? Is foot length an appropriate measurement comparison to height or is arm span a more appropriate measurement to compare with height. Also do other types of animals such as cats or dogs have similar kind of ratio of their body proportions? Part 3

In this investigation we used measurement, always being careful to note that it was to the nearest unit. We used the measurement unit of centimetre, a metric unit of measurement. We also looked at Statistics, specifically a Scale factor, which is the ratio of two lengths. In our case we compared the length of our feet to our height. We used this information to ascertain the height of the yowie. Another element of Statistics that was used was the Mean, which is a measurement of centre in a data set that adds together all scores and divides by the number of scores. It is also sometimes termed an average. We calculated the mean of our Scale factors to find the average as we felt it would...
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