Канал: Sciency Sergei

Rayleigh scattering on Lake Michigan

Rayleigh scattering on Lake Michigan

Infinite Equation

Infinite Equation

Circles, triangles, and ... sharks.

Circles, triangles, and ... sharks.

Find area of a square intersected by a circle

Find area of a square intersected by a circle

Find an angle in two circles.

Find an angle in two circles.

Rigid body motion. Part 2. Dynamics.

Rigid body motion. Part 2. Dynamics.

Area in quarter circle

Area in quarter circle

Rigid body motion. Part 1. Kinematics.

Rigid body motion. Part 1. Kinematics.

Introduction to vectors in physics

Introduction to vectors in physics

How to solve any problem in dynamics. Just follow these simple rules!

How to solve any problem in dynamics. Just follow these simple rules!

Things we can watch forever: others doing work

Things we can watch forever: others doing work

Things we can watch forever: water

Things we can watch forever: water

Things we can watch forever: fire

Things we can watch forever: fire

Covering a quad with circles

Covering a quad with circles

Sphere and line in nature. Is this geometry or anatomy?

Sphere and line in nature. Is this geometry or anatomy?

Geometry and nature: can we consider water surface as a plane?

Geometry and nature: can we consider water surface as a plane?

Median, bisectors and more. From Korea with love.

Median, bisectors and more. From Korea with love.

Geometry and nature: among straight lines

Geometry and nature: among straight lines

When you get stuck with a geometry problem, go to see the nature.

When you get stuck with a geometry problem, go to see the nature.

How to use Stewart's theorem without remembering it. Apollonius' and angle bisector theorems.

How to use Stewart's theorem without remembering it. Apollonius' and angle bisector theorems.

Calculate area using everything you know. Algebra, geometry, calculus.

Calculate area using everything you know. Algebra, geometry, calculus.

Two ways to find a segment in a triangle with a bisector.

Two ways to find a segment in a triangle with a bisector.

Another look at angle trisection

Another look at angle trisection

Trisecting an angle

Trisecting an angle

Square and angles

Square and angles

Pentagon, golden ratio, and angles of 18, 36, 54, and 72 degrees

Pentagon, golden ratio, and angles of 18, 36, 54, and 72 degrees

Tale of two regular pentagons.

Tale of two regular pentagons.

Count triangles, count similarities

Count triangles, count similarities

Geometry and nature. Can you hear the frogs?

Geometry and nature. Can you hear the frogs?

Who is responsible when problem is wrong?

Who is responsible when problem is wrong?

Pain of wrong solutions in geometry

Pain of wrong solutions in geometry

Facts to achieve a happy life with inscribed polygons.

Facts to achieve a happy life with inscribed polygons.

How to think in geometry - a look into Sergei's head.

How to think in geometry - a look into Sergei's head.

Mental math in geometry. Find angle x.

Mental math in geometry. Find angle x.

Find a side. Problem from Croatia.

Find a side. Problem from Croatia.

Find side of a quadrilateral

Find side of a quadrilateral

Circle and triangle inside of square. Find radius.

Circle and triangle inside of square. Find radius.

Circle in a tangent half circle. Find area.

Circle in a tangent half circle. Find area.

15-75-90 degree triangle. Find sides and area.

15-75-90 degree triangle. Find sides and area.

18-72-90 degree triangle. Find sides and area

18-72-90 degree triangle. Find sides and area

Everything (almost) you need to know to solve exponential equations

Everything (almost) you need to know to solve exponential equations

Find angle x in a quarter circle and two squares.

Find angle x in a quarter circle and two squares.

Tangent circles and a triangle. Find areas.

Tangent circles and a triangle. Find areas.

Sides of triangle and medians (side bisectors).

Sides of triangle and medians (side bisectors).

Find segment length in a square and two triangles

Find segment length in a square and two triangles

Half circle in a triangle. Find the radius.

Half circle in a triangle. Find the radius.

Find area of a square in a square and circles

Find area of a square in a square and circles

Find an angle in a square and a circle.

Find an angle in a square and a circle.

Find i^i. Complex numbers.

Find i^i. Complex numbers.

Find positive integer solutions: 1/x + 1/y = 1/5

Find positive integer solutions: 1/x + 1/y = 1/5

Find angle x in a triangle with midpoints.

Find angle x in a triangle with midpoints.

Annoying problem. x+1/x=-1. Find x^2021+1/x^2021.

Annoying problem. x+1/x=-1. Find x^2021+1/x^2021.

Find area of a triangle inside of a parallelogram.

Find area of a triangle inside of a parallelogram.

Circle in a circle. What's the area?

Circle in a circle. What's the area?

Two ways to solve a polynomial equation. 2x^4-3x^3-13x^2+3x+2=0

Two ways to solve a polynomial equation. 2x^4-3x^3-13x^2+3x+2=0

Find angle between triangle and square. 30-60-90 degree triangles.

Find angle between triangle and square. 30-60-90 degree triangles.

Find angle in a semicircle.

Find angle in a semicircle.

Find ratio of areas of squares inside another square.

Find ratio of areas of squares inside another square.

Most useful formula in theory of limits. L'Hôpital's rule.

Most useful formula in theory of limits. L'Hôpital's rule.

How good should a drawing in geometry be? Find a segment. Circle inscribed in triangle.

How good should a drawing in geometry be? Find a segment. Circle inscribed in triangle.

Compare 2^pi and pi^2. Two ways: algebra and calculus.

Compare 2^pi and pi^2. Two ways: algebra and calculus.

Angles, bisectors, symmetries, isosceles triangles

Angles, bisectors, symmetries, isosceles triangles

Is there a correct way to solve geometry problem?

Is there a correct way to solve geometry problem?

Square in a circle. Find distance.

Square in a circle. Find distance.

Monotonicity rules. How to compare numbers.

Monotonicity rules. How to compare numbers.

Find ratio of areas in circles and rectangles

Find ratio of areas in circles and rectangles

Find radius lost in triangles

Find radius lost in triangles

Trapezoid and circle - find an angle.

Trapezoid and circle - find an angle.

Find ratio of segments in triangles and inscribed circles.

Find ratio of segments in triangles and inscribed circles.

Find angle hidden in circles.

Find angle hidden in circles.

Find area of a square inside another square

Find area of a square inside another square

Find angle x in a triangle. Part 3. Trigonometry

Find angle x in a triangle. Part 3. Trigonometry

Find angle x in a triangle. Part 2

Find angle x in a triangle. Part 2

Find angle x in a triangle. Part 1

Find angle x in a triangle. Part 1

Find angle APC in equilateral triangle when BP^2=AP^2+CP^2

Find angle APC in equilateral triangle when BP^2=AP^2+CP^2

Physics: sliding object on the top of another.

Physics: sliding object on the top of another.

Physics: coin on a moving surface

Physics: coin on a moving surface

Find angle x in a triangle. Trigonometric approach.

Find angle x in a triangle. Trigonometric approach.

Solve exponential equation with absolute values. Easy!

Solve exponential equation with absolute values. Easy!

Find area of a triangle inside a square.

Find area of a triangle inside a square.

Find angle x lost in polygons.

Find angle x lost in polygons.

Logarithmic equation that is not as difficult as it seems.

Logarithmic equation that is not as difficult as it seems.

Find area among a square and four circles

Find area among a square and four circles

Find area in a circle

Find area in a circle

Find angle x in circles.

Find angle x in circles.

Equation that seems too difficult to solve.

Equation that seems too difficult to solve.

Find angle x. Pure geometric solution.

Find angle x. Pure geometric solution.

Find angle x. Mostly trigonometric solution.

Find angle x. Mostly trigonometric solution.

Insanely simple solution of a system of equations

Insanely simple solution of a system of equations

Find integer area in a rectangle. Mix of geometry and number theory. Who thought it would be fun?!

Find integer area in a rectangle. Mix of geometry and number theory. Who thought it would be fun?!

Chords and circle - find distance fast. Can you do it faster than me?

Chords and circle - find distance fast. Can you do it faster than me?

Transforming geometric sequence into arithmetic sequence and back.

Transforming geometric sequence into arithmetic sequence and back.

Find area of the parallelogram and radius of the circle

Find area of the parallelogram and radius of the circle

Trigonometric equation.

Trigonometric equation.

Find angle x. Triangles and quadrilaterals. Forgotten triangle congruency criterion.

Find angle x. Triangles and quadrilaterals. Forgotten triangle congruency criterion.

Combinatorics meets number theory

Combinatorics meets number theory

Find area among the circles.

Find area among the circles.

Find angle x. Circle, rectangle, and square. Use of symmetry in geometry.

Find angle x. Circle, rectangle, and square. Use of symmetry in geometry.

Solve parametric problem.

Solve parametric problem.

Solve inequality with square root and absolute value

Solve inequality with square root and absolute value

Find another angle x in a triangle.

Find another angle x in a triangle.

Solving logarithmic equation

Solving logarithmic equation

Find ratio of segment lengths inside a square. Method of coordinates.

Find ratio of segment lengths inside a square. Method of coordinates.

Find area of a quadrilateral in a very simple way.

Find area of a quadrilateral in a very simple way.

Find distance x between a point and a side of a trapezoid in two different ways.

Find distance x between a point and a side of a trapezoid in two different ways.

Productivity problem from 19th century

Productivity problem from 19th century

Calculate area of a quadrilateral. Use the method of coordinates.

Calculate area of a quadrilateral. Use the method of coordinates.

Find side x of a triangle.

Find side x of a triangle.

Find angle x. Geometry approach.

Find angle x. Geometry approach.

23. Find angle x. Trigonometry.

23. Find angle x. Trigonometry.

22. Another geometry problem - looking for an angle. Solution through trigonometry.

22. Another geometry problem - looking for an angle. Solution through trigonometry.

21. Sines and cosines of 18, 36, 54, and 72 degree angles.

21. Sines and cosines of 18, 36, 54, and 72 degree angles.

15. Life inverted: derivatives of inverse functions.

15. Life inverted: derivatives of inverse functions.

14. Global max and min on closed interval.

14. Global max and min on closed interval.

Find the angle

Find the angle

20. Geometry meets trigonometry

20. Geometry meets trigonometry

Mathcounts: counting random numbers - probability and number theory combined.

Mathcounts: counting random numbers - probability and number theory combined.

19. Equation that makes you think. Trigonometry and polynomial equations.

19. Equation that makes you think. Trigonometry and polynomial equations.

13. Going up and down. Finding max and min.

13. Going up and down. Finding max and min.

18. Where is tangent on unit circle? Simple tangent equations.

18. Where is tangent on unit circle? Simple tangent equations.

17. Simple equations for sin and cos.

17. Simple equations for sin and cos.

Mathcounts: Unfair game of dice

Mathcounts: Unfair game of dice

Mathcounts: Shooting darts with geometry - calculate probabilities geometric way

Mathcounts: Shooting darts with geometry - calculate probabilities geometric way

Mathcounts: Solving algebra problem in two ways.

Mathcounts: Solving algebra problem in two ways.

Mathcounts: Functional equations

Mathcounts: Functional equations

Mathcounts: Can you solve the puzzle?

Mathcounts: Can you solve the puzzle?

$Mathcounts: Number system conversion and periodic fractions$

Mathcounts: Number system conversion and periodic fractions

Mathcounts: Rhombus, rhombus, rhombus!

Mathcounts: Rhombus, rhombus, rhombus!

Mathcounts: Counting the balls and probability.

Mathcounts: Counting the balls and probability.

12. Pretty common functions

12. Pretty common functions

Mathcounts: Let's calculate area!

Mathcounts: Let's calculate area!

Mathcounts: Secrets of GCF and LCM

Mathcounts: Secrets of GCF and LCM

Mathcounts: merry go round and round and round

Mathcounts: merry go round and round and round

11. "Divide and differentiate!" Philip of Macedon

11. "Divide and differentiate!" Philip of Macedon

Mathcounts: flipping a coin

Mathcounts: flipping a coin

Mathcounts: counting dominos

Mathcounts: counting dominos

Mathcounts: equation with absolute value terms

Mathcounts: equation with absolute value terms

10. Nested and chained: superposition of functions and chain rule

10. Nested and chained: superposition of functions and chain rule

9. Simplicity Multiplicity: derivative of the product of functions

9. Simplicity Multiplicity: derivative of the product of functions

Kinematics 2

Kinematics 2

16. Adding and subtracting sines and cosines.

16. Adding and subtracting sines and cosines.

15. Long forgotten tangent: oddness of tangent, tangent of sum and difference

15. Long forgotten tangent: oddness of tangent, tangent of sum and difference

14. Algebra tricks. Another way to calculate cosine of 15 degrees.

14. Algebra tricks. Another way to calculate cosine of 15 degrees.

13. Example: sine, cosine, and tangent of 15 degrees

13. Example: sine, cosine, and tangent of 15 degrees

12. Double and triple angles

12. Double and triple angles

11. The second most important formula in trigonometry

11. The second most important formula in trigonometry

10. Are you odd or even? cos(-x) and sin(-x)

10. Are you odd or even? cos(-x) and sin(-x)

9. Getting our hands dirty: 90+x, 90-x, 180+x, and 180-x angles

9. Getting our hands dirty: 90+x, 90-x, 180+x, and 180-x angles

8. Radians!!! We finally meet you!

8. Radians!!! We finally meet you!

7. Quadrants, what are you?

7. Quadrants, what are you?

Kinematics 1

Kinematics 1

4. Little practice in vector arithmetics

4. Little practice in vector arithmetics

3. Let's paint - adding/subtracting vectors graphically

3. Let's paint - adding/subtracting vectors graphically

2. One plus two - can you add?

2. One plus two - can you add?

1. What are those pointy things?

1. What are those pointy things?

6. Back to the right triangle - angles of 45, 30, and 60 degrees

6. Back to the right triangle - angles of 45, 30, and 60 degrees

5. Simple life with 90-degree turns

5. Simple life with 90-degree turns

4. Chasing dog's tail - going in circles

4. Chasing dog's tail - going in circles

3. So long, Right Triangle - changing the definition

3. So long, Right Triangle - changing the definition

2. Family ties - relationships among functions

2. Family ties - relationships among functions

1. Our friends for the rest of life - sin, cos, tan, ...

1. Our friends for the rest of life - sin, cos, tan, ...

8. Building LEGO houses - Integration of linear combinations

8. Building LEGO houses - Integration of linear combinations

7. Power Trip in Reverse - integration of power functions

7. Power Trip in Reverse - integration of power functions

6. Uncertainty of Life - Intro to Integration

6. Uncertainty of Life - Intro to Integration

4. Subtracting parentheses ... NOOOOO!

4. Subtracting parentheses ... NOOOOO!

3. OMG! Parentheses!

3. OMG! Parentheses!

2. Rules, rules, rules ... How uplifting!

2. Rules, rules, rules ... How uplifting!

1. Simplest equations

1. Simplest equations

5. Freedom without limits - how to calculate derivatives in a jiffy

5. Freedom without limits - how to calculate derivatives in a jiffy

4. On a power trip - derivative of power functions

4. On a power trip - derivative of power functions

3. Ripples are getting stronger - derivatives are getting more complicated

3. Ripples are getting stronger - derivatives are getting more complicated

2. Very little bumps on the road - derivatives of insanely simple functions

2. Very little bumps on the road - derivatives of insanely simple functions

1. On a slippery slope - gentle intro into derivatives

1. On a slippery slope - gentle intro into derivatives