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arXiv:1510.00735v3 [math.NT] 14 Oct 2015
arXiv:1510.00735v3 [math.NT] 14 Oct 2015

... KEN ONO AND SARAH TREBAT-LEDER Abstract. We revisit the mathematics that Ramanujan developed in connection with the famous “taxi-cab” number 1729. A study of his writings reveals that he had been studying Euler’s diophantine equation a3 + b3 = c3 + d3 . It turns out that Ramanujan’s work anticipated ...
Cubic Thue equations with many solutions
Cubic Thue equations with many solutions

Triangle Inequalities
Triangle Inequalities

1.4: Measuring Segments and Angles
1.4: Measuring Segments and Angles

... Let OA and OB be opposite rays in a plane, OA, OB, and all the rays with endpoint O that can be drawn on one side of AB can be paired with the real numbers from 0º to 180º so that: a. OA is paired with 0º and OB is paired with 180º. b. If OC is paired with x and OD is paired with y, then mCOD = |x- ...
Analysis
Analysis

1346492101.
1346492101.

The Cartesian Plane and Functions - WBM
The Cartesian Plane and Functions - WBM

Embedded Figures Answer Key
Embedded Figures Answer Key

Ratios involving fractions
Ratios involving fractions

ÿþM i c r o s o f t   W o r d   - I M C 2 0 1 1 w e b   s o l u t i o n s
ÿþM i c r o s o f t W o r d - I M C 2 0 1 1 w e b s o l u t i o n s

... These solutions augment the printed solutions that we send to schools. For convenience, the solutions sent to schools are confined to two sides of A4 paper and therefore in many cases are rather short. The solutions given here have been extended. In some cases we give alternative solutions, and we h ...
HSC Mathematics Workshop 3
HSC Mathematics Workshop 3

... Taking it to the limit, in other words interest is compounded continuously, we have: 1 n ) = 2.71828... = e ...
Mathematics
Mathematics

... Two squares are congruent, if they have the same side length. Two rectangles are congruent, if they have the same length and breadths. Two circles are congruent, if they have the same radii. Two equilateral triangles are congruent, if they have same measurements of side. Two triangles are congruent, ...
Chapter 1 – Exponents and Measurement Exponents – A shorthand
Chapter 1 – Exponents and Measurement Exponents – A shorthand

L. Caporaso COUNTING RATIONAL POINTS ON ALGEBRAIC
L. Caporaso COUNTING RATIONAL POINTS ON ALGEBRAIC

LESSON PLAN School Unit : Junior High School Subject
LESSON PLAN School Unit : Junior High School Subject

... a. Determine the formula of Pythagorean theorem by investigation b. Use Pythagorean theorem to compute the length of a right triangle side if two other sides are known c. Determine the proportion of special right triangle sides (the measure of one angle is 300, 450, and 600 ) d. Find three number ar ...
Cycloidal Areas without Calculus
Cycloidal Areas without Calculus

Bloom`s Taxonomy applied to understanding the Pythagorean
Bloom`s Taxonomy applied to understanding the Pythagorean

... 3. Use the Pythagorean Theorem to explain why the graph of x 2  y 2  r 2 is a circle. 4. Create a story problem the solution of which involves use of the Pythagorean Theorem. 5. Describe how you would teach a younger sibling the concept and use of the Pythagorean Theorem. Communicate your understa ...
MATH 31 CLASS NOTES XII – Section 5
MATH 31 CLASS NOTES XII – Section 5

Right Triangle Trigonometry
Right Triangle Trigonometry

Name_______________________________________ Date
Name_______________________________________ Date

2500 years of very small numbers - University of Hawaii Mathematics
2500 years of very small numbers - University of Hawaii Mathematics

This is first slide - International Association for
This is first slide - International Association for

An Ancient Diophantine Equation with applications to Numerical
An Ancient Diophantine Equation with applications to Numerical

Applications of Pell`s Equation
Applications of Pell`s Equation

Accelerated Maths
Accelerated Maths

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John Wallis

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