First blog post!
Problem (from Delta Maths 2nd Edition by David Barton and Stuart Laird):
In classical times, artists were aware of the effect of proportion on the appearance of the human body, architecture and nature. Leonardo da Vinci's famous drawing of 'Vitruvian man' implies that the distance between outstretched fingertips and the height from the top of the head to the soles of the feet should be the same. It also suggests that the navel is naturally the central point of the body. Approximate the diagram by assuming that the top two corners of the square lie on the circle.
Suppose a person who fits these proportions has a height of 175 mm. Calculate the distance from their navel to the sole of each foot.
Have a go at this problem if you haven't solved it already. Have fun!
Hints:
- This distance is consequently the radius of the circle.
- Given that 175mm is the height, can you write this as a combination of x and some angles?
- Use sine rule and cosine rule and double angle cosine formula.
Briefly look at part of the solution if stuck for several hours (I know the feeling - I struggled with this problem for two days without help and several attempts😅).
Full solution:
(Right click and view image in new tab)
MJGM
