Alice's Mathematical Adventures

Alice finds herself in a mathematical puzzle in Wonderland, where the Queen of Hearts claims that 64 is the same as 65. Alice is challenged to prove the Queen wrong using two chessboards and soldiers shaped as trapezoids and triangles. By calculating slopes, Alice discovers a hidden gap, revealing the Queen's trick. The puzzle involves Fibonacci numbers and their properties, which create deceptive slopes. The video explores these mathematical concepts and concludes with a nod to Lewis Carroll's work.

What does Alice overhear the Queen of Hearts claiming?

• 64 is the same as 65

• 64 is twice 65

• 64 is greater than 65

• 64 is less than 65

What shapes do the card soldiers form on the chessboard?

• Squares and circles

• Triangles and rectangles

• Trapezoids and triangles

• Hexagons and pentagons

How does Alice determine the Queen's trick?

• By rearranging the chessboard

• By measuring the soldiers

• By calculating the slopes

• By counting the soldiers

What is the slope of the trapezoid soldier's diagonal side?

• 0.375

• 0.3

• 0.5

• 0.4

What mathematical series is mentioned in the puzzle?

• Prime numbers

• Arithmetic series

• Fibonacci series

• Geometric series

What property of Fibonacci numbers is highlighted in the puzzle?

• They are all odd

• They form a perfect square

• They are all even

• Their squares relate to products of adjacent numbers

What does Alice use to get a closer look at the puzzle?

• A magnifying glass

• A shrinking potion

• A telescope

• A microscope

What does Alice find between the triangles and trapezoids?

• A circle

• A square

• A hexagon

• A parallelogram

What does the ratio between successive Fibonacci numbers converge to?

• The square root of two

• Euler's number

• Pi

• The golden ratio

Who is the author of 'Alice in Wonderland'?

• J.K. Rowling

• Lewis Carroll

• Mark Twain

• Charles Dickens