The-Nature-of-Mathematics .pdf

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1. The Nature of
Mathematics

2. Mathematics
•Comes from the Greek work “mathema”, which means
“that which is learnt” or “lesson”
•The science of structure, order, and relations that has
evolved from elemental practices of counting, measuring,
and describing the shapes and characteristics of objects.
(Encyclopedia Britannica)
•Numbersare the heart of mathematics

3. Nature of Mathematics
•A science of Measures
•Intellectual game
•The art of drawing conclusions
•A tool subject
•A system of logical procedure
•An intuitive method

4. Mathematics as a Science of Patterns
“A mathematician, like painter or a poet, is a master of
patterns. If his pattern are more permanent than theirs, it is
because they are made with ideas”
-Hardy, 1992

5. Pattern
•A visible regularities in the world or in a man-made design
•Its elements are repeated in a predictable manner.
Common patterns:
❖Logic
❖Symbol
❖Number
❖Word

6. Logic Patterns
•Deals with characteristics of various objects
Which of the shapes below continues the sequence:

7. Answer:

8. Logic Pattern

9. Answer:

10. Logic Patterns

11. Answer:

12. Number Patterns
Find the next number in the sequence:
1.11, 13, 17, 19, 23, _____
2.5, 7, 10, 15, 22, _____
3.12, 13, 15, 18, 22, _____
4.7, 20, 47, 94, 167, _____
5.1, 4, 2, 8, 6, 24, 22, _____

13. Answers:
1.25
2.33
3.27
4.272
5.88

14. Patterns in
Nature
Bilateral symmetry or Mirror
symmetry

15. Patterns in
Nature
Radial symmetry or Rotational
symmetry

16. Patterns in
Nature
Fractal

17. Patterns in
Nature
SPIRAL

18. Patterns in Nature
WAVES AND DUNES

19. Patterns in
Nature
TESSELLATIONS

20. Patterns in Nature
CRACKS OR FRACTURES

21. Patterns in Nature
STRIPES AND SPOTS

22. Patterns in Nature
World Population
A=Pe
rt
•equation for population growth, where
A is the size of the population after it has grown,
P is the population’s starting point, r is the rate of
growth, and t is the passage of time
e is Euler’s constant and that it has a value of roughly
2.718

23. Patterns in Nature
World Population (Example)
The growth model A = 800,000,000 e
0.015t
describes the
population of a country, t years after 2010.
a.What was the population of the country in 2010?
-800 million
b.What will be the population in 2030?
-approximately 1.08 billion

24. Patterns in Nature
Exponential Decay
N = N
0e
-kt
where
N is the amount remaining after time t,
N
0as the initial amount, k as the decay constant, and
e as Euler’s constant with the approximated value of
2.718

25. Patterns in Nature
Exponential Decay (example)
A certain medication has a half-life of 8 hours. If a patient is
given an initial dose of 100 mg, how much of the
medication will remain in their body after 24 hours?
Answer: After 24 hours, the patient’s body will still contain
the medicine approximately 12.52 mg

26. Exercises:
Determine what comes next in the given patterns.
1.A, C, E, G, I, ___ 6. 15, 10, 14, 10, 13, 10, ___
2.3, 6, 12, 24, 48, 96, ___ 7. 27, 30, 33, 36, 39, ___
3.41, 39, 37, 35, 33, ___ 8. CSD, ETF, GUH, _____
4.22, 21, 25, 24, 28, 27, ___ 9. O, T, T, F, F, S, S, E, ___
5.1, 8, 27, 64, 125, ___ 10. 1, 3, 9, 27, 81, ___