Euclid's Elements
What is the modern word for what Euclid called, "common notions"?
Axiom
(This is not one of Diophantus' problems.) Prove 0.9 repeating equals 1 and explain what axioms you use in the process
x = 0.99999
10=9.999999
9x=9
x=1
The various properties of equalities, which are demonstrated by Diophantus though he didn't call them that.
What is the standard form of Quadratic Equations?
ax2+bx+c
How do you say "f(x)"
f of x
what is f(7)?
F(2)= F(2-1) +3
F(17) = e
e - 45
(for those who don't know e is eulers number)
Who was Euclid? what is he known as?
Euclid is a greek mathematician know as the father of geometry
to find two numbers whose sum and difference of squares are given (20, 80).
x+y=20, x2-y2=80.
who wrote Quadratrure of the parabola? (hint: he has a spiral named after him.)
Archimedes
Where is chalkboard bold used in math.
To denote sets that are previously specified in greater mathematics
What is the name of the bar in a fraction
vinculum
What is non-euclidean geometry? why do we call it that? and can you give two examples of what might be possible in non-euclidean geometry?
answers may vary.
6
What is the gravitational constant that is the coefficient of x2 when calculating how things fall?
-4.9 or -16
(depending on metric vs. imperial)
What operations do you know? (like +, -, etc. (I can't give you all of them) (there is a minimum requirement that I'm looking for.)
addition, subtraction, multiplication, exponenciation, division, logaritms, sin, cos, tan, (the inverse trig functions), and factorial. (answers may vary.)
what is roughly the number of digits in 3^^^3 (further explanation is available if necessary)
x * 10l * 10^3,640,000,000,000
{1≤x<10} {Log10(3)≤l<10*Log10(3)}
Euclid's common notions are the following, which is missing?
Things which are equal to the same thing are also equal to one another
If equals be added to equals, the wholes are equal
Things which coincide with one another are equal to one another
The whole is greater than the part
If equals be subtracted from equals, the remainders are equal
write an algebraic proof for why 0.9 repeating = 1
I can check your work and write mine on the board.
What is one application of what calculating the area of a parabola is helpful? and why it might be helpful for us to be able to approximate the area of them?
Some satellite dishes are parabolas, you need to know the area so you know how much of the given material you need to buy.
what is 1000.432% of 10?
100.0432
Solve for the quadratic formula (solve for x) given the standard form of quadratic equations (ax2+bx+c) **You must show your work
Did you?
What are Euclid's common notions? (the axioms, greeks just didn't have that word) and explain how 3 of them are used in modern geometry?
answers may greatly vary, however the whole is greater than the part is used all the time to break down (composite) shapes into easier ones, if equals are added to equals, the whole is equal, (if a=b, & c=d, a+c=b+d), and the transitive property is one of Euclid's common notions but he doesn't call it that (if a = b, and b = c, then a = c)
x2+y=a2, xy + a2=b2, xy- a2=c2
Is this solvable?
no?
What shape do we use to approximate the area of a parabola? and why?
We use triangles because they are easy to calculate the area of, we can manipulate them in many ways, and they can tile the plane.
Explain why 1+1=2
In the set of Natural numbers every numbers successor can be attained by adding one, one is two's predecessor, and thus 1 + 1 = 2. Answers may vary.
Past the set of complex numbers there is a set of sets called hypercomplex numbers that includes higher dimensional numbers, Quaternions are the first of those numbers, why is this significant?
because beginning at the 4th dimension numbers start to lose the property of certain axioms. Quaternions lose their commutativity.