MATHS DI 2
Investigation #4
Finding the second derivative and A, B
Finding the equation of the line which passes through A and B
Finding C and D, the other points of intersection
Ratio of distance between CA, AB and BD
Notice how if
Therefore, the function will not have 2 points of inflection, thus will not be a Golden Quartic, and points A and B, the non-stationary points of inflection will be non-existent and hence, the distance between the points will also be non-existent, as shown below:
Investigation #5
Finding A and B, the non-stationary points of inflection
Finding the equation of the line which passes through A and B
Finding C and D, the other points of intersection
Ratio of distances between CA, AB, and BD
f) Conjecture about the ratio of the distance between the line that passes through the points of inflection of a Golden Quartic
If a Golden Quartic, from left to right, has a line that passes through A and B, it’s points of inflection, and C and D are the other points of inflection, then the ratio of the distance from CA:AB:BD will be 1:1.618:1
g) Significance of the ratio of 1:1.618:1
1:1.618:1 is the Golden Ratio. In nature, this can be seen in bee hives, where the ratio of male bees: female bees is 1:1.618, and in flowers where opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation (Jarus, 2013). The golden ratio is deemed the most visually appealing ratio; in humans, the ratio between the shoulders to the finger tips to the elbows to the finger tips is approximately 1:1.618, similarly the distance from the head to the feet in comparison to the head to the belly button is also 1:1.618, and distance between the eyes verses the distance between the ears is in a ratio of 1:1.618, and hence this ratio is vital for humans to find those more appealing mates, and ensuring
Finding the second derivative and A, B
Finding the equation of the line which passes through A and B
Finding C and D, the other points of intersection
Ratio of distance between CA, AB and BD
Notice how if
Therefore, the function will not have 2 points of inflection, thus will not be a Golden Quartic, and points A and B, the non-stationary points of inflection will be non-existent and hence, the distance between the points will also be non-existent, as shown below:
Investigation #5
Finding A and B, the non-stationary points of inflection
Finding the equation of the line which passes through A and B
Finding C and D, the other points of intersection
Ratio of distances between CA, AB, and BD
f) Conjecture about the ratio of the distance between the line that passes through the points of inflection of a Golden Quartic
If a Golden Quartic, from left to right, has a line that passes through A and B, it’s points of inflection, and C and D are the other points of inflection, then the ratio of the distance from CA:AB:BD will be 1:1.618:1
g) Significance of the ratio of 1:1.618:1
1:1.618:1 is the Golden Ratio. In nature, this can be seen in bee hives, where the ratio of male bees: female bees is 1:1.618, and in flowers where opposing spirals of seeds, have a 1.618 ratio between the diameters of each rotation (Jarus, 2013). The golden ratio is deemed the most visually appealing ratio; in humans, the ratio between the shoulders to the finger tips to the elbows to the finger tips is approximately 1:1.618, similarly the distance from the head to the feet in comparison to the head to the belly button is also 1:1.618, and distance between the eyes verses the distance between the ears is in a ratio of 1:1.618, and hence this ratio is vital for humans to find those more appealing mates, and ensuring