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Fermi question

How many hairs on a human head ?

Tiffany Clarke

on 20 August 2013

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Transcript of Fermi question

Fermi Journal

By Angus, Tiffany and Yunxiao.
Day One
Today our group got a Fermi question. What was the question? It was "How many hairs are on a human's head (the scalp)?" First, we found out who Enrico Fermi actually was. We found out that he was an Italian physicist and mathematician. Enrico tried to solve questions that didn't have an exact answer.

Day 2
This time we discussed if any of us had any solutions to figure out our Fermi question. We figured out one idea.
Our solution: Find how many hairs are in a certain small area of the head. Then we can use this combined with the area of the head to find the number of hairs on a human head. This result could vary depending on:
- gender
- hair colour
- age
- nationality
- thickness of hair

Who was Enrico Fermi?
Enrico Fermi was an Italian physicist and mathematician. He was born on the 29th September 1901 and died on the 28th November 1954. He was known for winning the Nobel Prize for Physics in 1938. Other prizes included:
Matteucci Medal (1926)
Hughes Medal (1942)
Medal for Merit (1946)
Franklin Medal (1947)
Rumford Prize (1953)
Enrico Fermi hard at work.
Day Four
We decided to start solving our problem. The problem is, we don't know how to find the area of a circular shape (the head). That meant we had to search it up on the internet. We found out that it was pi * r * r. First, we measured each other's scalp circumference. Daniel's was 60cm, Fahad's was 55cm and Yunxiao's was 55cm. The average circumference was about 56.666667cm.
Day 5
This time we tried a solution. We used a cube that was 2cm x 2cm. We put it on Daniel's head and found out that he had approximately 150 strands of hair inside the cube. Now we need to find the radius of the scalp. The diameter was 15cm. That meant that the radius was 7.5 cm. 7.5 cm equaled to 56.25 cm . To find out the area now, we need to multiple 56.25cm by π (3.14). This equals 176.625cm.
If you can read this we owe you $10000000000000000000000000000000000000000000000000
Day 6
Angus is back!!!

Today we (more like I - aka Angus) came up with a new theory on how we could work out the area of our head (scalp). Our first solution didn't work. Since our head (scalp) wasn't an exact circle, the maths we used didn't work. Now Angus thought that if we put a piece of paper over our head and cut it to the size of Daniels scalp. Then if we measure it after flattening it out, it might work.
Day Seven
Skip a Day
We completed our journal diary entry from yesterday. We started tested our new theory on how to find the area of Daniels scalp by creating a paper helmet.
The biggest piece of paper you will ever see in your life
This is also the biggest writing you will see in your life.
And the biggest arrow you will see in your life.
If you can see this u r genius

Day 9

Tiffany is back. Yay!
Today we are going to find the area of Daniels paper helmet. We are using a 1 x 1 cm grid to find out the area of his head as the theory we used didn't work as his head is an oval, not a circle.
Tiffany, Yunxiao and Angus are amazing

Day Ten
Today Angus finished finding out the area of Daniels scalp.

The total area was 796.5 cm²

Angus also noticed that while he was away that the boys thought that the cube we counted the hairs in was 2 cm x 2 cm (on the outside, not the inside, and it was wrong anyway), however they were wrong it was 1.5 cm x 1.5cm on the inside and was correct (see photo).

So we divide the surface area by 2.25 (the area of the hair we tested) and multiply it by 150 (the number of hairs in this space). And we'll get an answer...
Photos from Day 10
The cut up and glued up paper hat.
It's actually 1.5 cm by 1.5 cm...
Back to work...
796.5 / 2.25 x 150 or
hairs on a human head
or so we think...
When we looked up the answer on Google, we found that a reasonable answer is between 90 000 and 150 000. We were about half of that, so quite a bit off. We thought that Fahad and Daniel had the wrong answer, because they used the wrong formula (area of head x no of hairs in a 2.25 area, which is wrong because you are literally multiplying the area by a random number, it's a bit complicated, ask Angus if you don't understand) but they had a more reasonable answer by a fluke, however we had the right process but the wrong numbers.

We think we went wrong when we counted the amount of hairs inside the cube (well, they, because Angus is writing this) or when we found the area of Daniel's scalp.
Blank slide
(This time, really. We swear that this is the end, no ifs, ands, buts, or maybes. THIS IS THE END!)
Photos from Day 7
or ZERO if you're bald
Note: The sentence '7.5 cm² equaled to 56.25 cm²' does not make sense. After we reviewed this we could not work out how we got this and why we wrote it. We could not delete it because it left out information. We apologise for the inconvenience.
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