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Maths
October 14th, 2013 (December 14th, 2013)
illustration

illustration (attribution, if any possible, is at the end of the article)

Maths…
(please bear with me)

Attached is a math problem (see image)… about finding the number on which the car is parked: the four spaces on the left are numbered 16, 06, 68, 88 and the space on the right is numbered 98.

Of course, everyone with decent mathematical background will know already that there's no solution to such a problem, unless constraints are added.

From a 5-points data set 
data = {{1, 16}, {2, 06}, {3, 68}, {4, 88}, {6, 98}}
I can fit a polynomial
curve = Fit[data, {1, x, x^2, x^3, x^4}, x]
which returns
curve = 322.4 – 557. x + 311. x^2 – 65. x^3 + 4.6 x^4
and I can then consider that, for x=5,
the car is parked on number 62.4
[graph attached]

But I may as well fit a 6-points data set
data = {{1, 16}, {2, 06}, {3, 68}, {4, 88}, {5, y},  {6, 98}}
with one extra degree available for the polynomial
curve = Fit[data, {1, x, x^2, x^3, x^4, x^5},  x]
and I can associated any number y to the parking space:
curve ≈ 0.00385842 x^3 (47169.6 – 1025.9 y) + 0.000118395 x^5 (21960.5 – 351.93 y) + 0.104828 x (2722.54 – 128.782 y) + 0.408248 (–127.373 + 14.6969 y) + 0.0209657 x^2 (–17409.4 + 516.717 y) + 0.000683172 x^4 (–54159.1 + 975.84 y)

For e.g. y = 1000, the polynomial becomes
curve(y=1000) = 5948. – 13214.6 x + 10468.3 x^2 – 3776.33 x^3 + 629.667 x^4 – 39.0667 x^5
It still fits all the data given, and I can then consider that, for x=5,
the car is parked on number 1000
[graph attached]

Or I can look at the math problem from another angle,
and the solution is less academic…
But is it any more valid?


#Buddhism  
h/t +Rajesh BK