Lesson 1 + quiz items

• Who invented the first equation?

  Egyptians
• Who invented geometry?

  Ancient Greece
• Who invented negative numbers?

  China
• Where was zero first used?

  India
• Where did the first book of algebra come from

  Persia
• It is the study of mathematics with its own sake

  Pure mathematics
• It is the mathematics where it is used to solve real-life problems

  Applied mathematics
• what proves that perfect order exists in the universe?

  Mathematical patterns
• ratio of golden ratio

  1.618
• He was a mathematician who discovered this (1,1,2,3,5,8....) sequence of numbers.

  Fibonacci
• It is comprised of Fibonacci numbers where it also has the same pattern as the human body.

  Pentagram
• What is an example of a golden section?

  DNA spiral
• how many notes are there per octave?

  13
• It is about mathematics as a system of knowing or understanding or surroundings


  Mathematics in the Modern World
• These explain why some systems in nature are self-similar, such as ferns.

  Fractals
• "Fractals" is a term contracted from the words?

  fraction and dimensional
• This type of mathematics gives us clues about the flow of water and the nature of the weather system

  butterfly effects and strange attractors
• the processes of reflection, rotation, and scaling are seen to be operating in nature to generate biological forms.


  affine transformations
• it can be found in nature such as the hexagonal arrangement of a snowflake

  geometry and symmetry
• are seen to occur naturally in snail shells, nautilus, and galaxies.

  Spirals
• Are certain areas of math such as differential calculus can be shown to govern how populations grow and collapse

  population dynamics
• These indicate a sense of structure and organization and from this perspective, some people see an intelligent design in the way that nature forms

  patterns
• This type of symmetry is when the left and right portions of things are identical.

  line or bilateral symmetry
• It is the property of a shape or thing, where it looks the same after some rotation by a partial turn.

  rational symmetry
• He is the man famous for breaking the Enigma code during WWII and for making the theory that chemical reactions and diffusion processes in cells determine these growth patterns in animals.

  Alan Turing
• what do you call the shell of a snail?

  protoconch
• this follows the rule that as the distance from the spiral center increases, the amplitudes of the angles formed to the radii to the point and the tangent to the point remain constant.

  equiangular spiral
• what is the formula for exponential growth?

  A=Pe^rt
• it is an ordered list of numbers called terms that may have repeated value

  sequence
• The Fibonacci sequence is named after the Italian mathematician?

  Leonardo of Pisa
• it is also known as the golden ratio

  Phi
• this can be expressed as the ratio between two numbers if the latter is also the ratio between the sum and the larger of the two numbers.

  golden ratio
• Who stated, "How is it possible that mathematics, a product of human thought that is independent of experience, fits so excellently the objects of reality"?

  Albert Einstein
• study of numbers and putting them into equationsin the form of variables

  structures
• the rules of how vectors and matrices relate to each other are captured in?

  linear algebra
• branch of mathematics that studies integers and arithmetic functions. It also studies the features of everything in the last section on numbers like prime numbers.

  number theory
• value of golden ratio


  1.618
• value of golden spiral in DNA


  1.619 or 34/21
• looks at the properties of certain structures like trees, graphs, and other things that are made of discrete chunks that you can carry


  combinatorics
• study of a set of different elements present in a group. An example of this would be a Rubik's cube, an example of a permutation group.

  group theory