Labelled diagram of skull anatomy illustrating basic osteology, with numbered identifiers for structures such as nasal bones, zygomatic processes, and dental alveoli. --- UWA DMF Radiology Dr Dayea Oh Basic Osteology of the Skull 1. anterior nasal spine 2. interseptal bone 3. crestal alveolar bone 4. inferior turbinate (concha) 5. cartilaginous nasal septum 6. inferior process of ethmoid bone 7. nasal fossa 8. infraorbital foramen 9. zygomatic process of maxilla 10. mental ridge 11. mental foramen 12. external oblique ridge 13. retromolar trigone 14. zygomatico-maxillary suture 15. zygomatic bone 16. zygomatico-temporal suture 17. zygomatic process of temporal bone 18. nasal bone 19. zygomatico-frontal suture  Labelled diagram of skull anatomy illustrating basic osteology, with numbered identifiers for structures such as nasal bones, zygomatic processes, and dental alveoli. #### Basic Osteology of the Skull 1. anterior nasal spine 2. interseptal bone 3. crestal alveolar bone 4. inferior turbinate (concha) 5. cartilaginous nasal septum 6. inferior process of ethmoid bone 7. nasal fossa 8. infraorbital foramen 9. zygomatic process of maxilla 10. mental ridge 11. mental foramen 12. external oblique ridge 13. retromolar trigone 14. zygomatico-maxillary suture 15. zygomatic bone 16. zygomatico-temporal suture 17. zygomatic process of temporal bone 18. nasal bone 19. zygomatico-frontal suture Labelled diagram of skull anatomy illustrating basic osteology. The image displays an anterior view of a human skull with numbered callouts pointing to specific anatomical structures. A legend below the diagram lists the corresponding names for numbers 1 through 19, including: anterior nasal spine, interseptal bone, crestal alveolar bone, inferior turbinate (concha), cartilaginous nasal septum, inferior process of ethmoid bone, nasal fossa, infraorbital foramen, zygomatic process of maxilla, mental ridge, mental foramen, external oblique ridge, retromolar trigone, zygomatico-maxillary suture, zygomatic bone, zygomatico-temporal suture, zygomatic process of temporal bone, nasal bone, and zygomatico-frontal suture. Student Name: 1. common carotid artery 2. external carotid artery 3. internal carotid artery 4. facial artery 5. inferior alveolar artery 6. internal maxillary artery 7. posterior superior alveolar arteries 8. infraorbital artery 9. labial artery 10. incisive artery UWA DMF Radiology Dr Dayea Oh   1. common carotid artery 2. external carotid artery 3. internal carotid artery 4. facial artery 5. inferior alveolar artery 6. internal maxillary artery 7. posterior superior alveolar arteries 8. infraorbital artery 9. labial artery 10. incisive artery Anatomical diagram of the arterial supply to the mandible and maxilla. The illustration shows the vascular tree originating from the common carotid artery (1), branching into the external carotid artery (2) and internal carotid artery (3). The external carotid artery gives rise to the facial artery (4), inferior alveolar artery (5), internal maxillary artery (6), posterior superior alveolar arteries (7), infraorbital artery (8), labial artery (9), and incisive artery (10). Labels are numbered 1 through 10 and correspond to a legend at the bottom left. Legend table listing the anatomical labels for the diagram above. It contains two columns: numbers 1-10 on the left and corresponding artery names on the right (e.g., '1. common carotid artery', '2. external carotid artery', etc.). Student Name: Maxilla 1. hard palate 2. infundibulum 3. ostium of nasolacrimal canal 4. inferior turbinate 5. middle turbinate 6. nasal bone 7. nasolacrimal canal 8. frontal sinus 9. sphenoid sinus 10. pituitary fossa 11. medial pterygoid plate 12. lateral pterygoid plate 13. hamular process of medial pterygoid plate (hamulus) 14. maxillary tuberosity 15. incisive foramen 16. median maxillary suture (midpalatal suture) 17. palatal process of maxilla 18. palato-maxillary suture (transverse) 19. shadow of nasolacrimal duct 20. palatine bone 21. greater palatine foramen 22. lesser palatine foramen 23. posterior nares 24. foramen of Stenson 25. incisive canal 26. foramen of Scarpa     #### Maxilla 1. hard palate 2. infundibulum 3. ostium of nasolacrimal canal 4. inferior turbinate 5. middle turbinate 6. nasal bone 7. nasolacrimal canal 8. frontal sinus 9. sphenoid sinus 10. pituitary fossa 11. medial pterygoid plate 12. lateral pterygoid plate 13. hamular process of medial pterygoid plate (hamulus) 14. maxillary tuberosity 15. incisive foramen 16. median maxillary suture (midpalatal suture) 17. palatal process of maxilla 18. palato-maxillary suture (transverse) 19. shadow of nasolacrimal duct 20. palatine bone 21. greater palatine foramen 22. lesser palatine foramen 23. posterior nares 24. foramen of Stenson 25. incisive canal 26. foramen of Scarpa Lateral radiographic view of the maxilla with numbered labels pointing to anatomical structures. Labels include: 3 ostium of nasolacrimal canal, 4 inferior turbinate, 5 middle turbinate, 6 nasal bone, 7 nasolacrimal canal, 8 frontal sinus, 9 sphenoid sinus, 10 pituitary fossa, 11 medial pterygoid plate, 12 lateral pterygoid plate, 13 hamular process of medial pterygoid plate (hamulus), 14 maxillary tuberosity, and 15 incisive foramen. An X-ray beam is shown entering from top right. Occlusal view of the maxilla showing dental arches and palatal structures. Numbered labels include: 1 hard palate, 16 median maxillary suture (midpalatal suture), 17 palatal process of maxilla, 18 palato-maxillary suture (transverse), 19 shadow of nasolacrimal duct, 20 palatine bone, 21 greater palatine foramen, 22 lesser palatine foramen, 23 posterior nares, 24 foramen of Stenson, 25 incisive canal, 26 foramen of Scarpa. Close-up inset diagram of the anterior maxilla region showing detailed anatomy. Labels point to: 24 foramen of Stenson, 25 incisive canal, 26 foramen of Scarpa, 15 incisive foramen, and 16 median maxillary suture (midpalatal suture). Numbered list table correlating numbers on diagrams with anatomical terms: 1 hard palate, 2 infundibulum, 3 ostium of nasolacrimal canal, 4 inferior turbinate, 5 middle turbinate, 6 nasal bone, 7 nasolacrimal canal, 8 frontal sinus, 9 sphenoid sinus, 10 pituitary fossa, 11 medial pterygoid plate, 12 lateral pterygoid plate, 13 hamular process of medial pterygoid plate (hamulus), 14 maxillary tuberosity, 15 incisive foramen, 16 median maxillary suture (midpalatal suture), 17 palatal process of maxilla, 18 palato-maxillary suture (transverse), 19 shadow of nasolacrimal duct, 20 palatine bone, 21 greater palatine foramen, 22 lesser palatine foramen, 23 posterior nares, 24 foramen of Stenson, 25 incisive canal, 26 foramen of Scarpa. Student Name: UWA DMF Radiology Dr Dayea Oh 1. lateral fossa 2. maxilla 3. vertical process of maxilla 4. floor of nasal fossa 5. vomer bone 6. palato-maxillary suture 7. palatal bone 8. posterior nasal spine 9. sinus recess / alveolar recess of sinus 10. maxillary sinus 11. bony septum of maxillary sinus 12. anterior nasal spine   1. lateral fossa 2. maxilla 3. vertical process of maxilla 4. floor of nasal fossa 5. vomer bone 6. palato-maxillary suture 7. palatal bone 8. posterior nasal spine 9. sinus recess / alveolar recess of sinus 10. maxillary sinus 11. bony septum of maxillary sinus 12. anterior nasal spine Labelled anatomical diagram of the maxilla and nasal cavity showing cross-sections. Key structures include: (1) lateral fossa, (2) maxilla, (3) vertical process of maxilla, (4) floor of nasal fossa, (5) vomer bone, (6) palato-maxillary suture, (7) palatal bone, (8) posterior nasal spine, (9) sinus recess / alveolar recess of sinus, (10) maxillary sinus, (11) bony septum of maxillary sinus, and (12) anterior nasal spine. Numbered legend table listing anatomical structures corresponding to labels in the diagram above. Entries include: 1. lateral fossa, 2. maxilla, 3. vertical process of maxilla, 4. floor of nasal fossa, 5. vomer bone, 6. palato-maxillary suture, 7. palatal bone, 8. posterior nasal spine, 9. sinus recess / alveolar recess of sinus, 10. maxillary sinus, 11. bony septum of maxillary sinus, 12. anterior nasal spine.  Labelled anatomical diagram of the mandible (jawbone) showing numbered callouts pointing to specific structures. The diagram includes a legend below with corresponding names for each number: 1. mental ridge, 2. mandibular symphysis, 3. mental foramen, 4. mandibular body, 5. external oblique ridge, 6. angle of mandible, 7. retromolar trigone, 8. ramus, 9. neck of condyle, 10. head of condyle, 11. sigmoid notch, 12. coronoid process, 13. medial sigmoid depression, 14. mandibular foramen, 15. lingula. Student Name: 1. coronoid process 2. sigmoid notch 3. head of condyle 4. medial sigmoid depression 5. mandibular foramen 6. angle of mandible 7. inferior cortex of mandible 8. digastric fossa 9. submandibular (salivary gland) fossa 10. mylohyoid (internal oblique) ridge 11. inferior genial tubercle of geniohyoid muscle 12. superior genial tubercle of genioglossus muscle 13. accessory lingual foramen for lingual vessels (lingual foramen) UWA DMF Radiology Dr Dayea Oh   1. coronoid process 2. sigmoid notch 3. head of condyle 4. medial sigmoid depression 5. mandibular foramen 6. angle of mandible 7. inferior cortex of mandible 8. digastric fossa 9. submandibular (salivary gland) fossa 10. mylohyoid (internal oblique) ridge 11. inferior genial tubercle of geniohyoid muscle 12. superior genial tubercle of genioglossus muscle 13. accessory lingual foramen for lingual vessels (lingual foramen) Labelled anatomical diagram of the mandible showing numbered callouts for specific structures. Visible labels include: 1. coronoid process, 2. sigmoid notch, 3. head of condyle, 4. medial sigmoid depression, 5. mandibular foramen, 6. angle of mandible, 7. inferior cortex of mandible, 8. digastric fossa, 9. submandibular (salivary gland) fossa, 10. mylohyoid (internal oblique) ridge, 11. inferior genial tubercle of geniohyoid muscle, 12. superior genial tubercle of genioglossus muscle, and 13. accessory lingual foramen for lingual vessels (lingual foramen). The image includes text 'Student Name:' at the top left. Listed key-value pairs defining the terms used in the diagram above. Entries are numbered 1 through 13 with corresponding anatomical definitions such as 'coronoid process', 'sigmoid notch', etc. Student Name: **Exercises** - Identify the type of x-ray - Identify anatomical structures / landmarks **Example)** **Q. Type of x-ray?** A: Periapical radiograph (PA) of 35, 34, 33 $\Rightarrow$ In radiology, Tooth $\#$ is counted from 18-28 (right to left), 38-48 (left to right) **Q. Anatomical structures/landmarks?** A: - 1. Mylohyoid ridge / internal oblique ridge - 2. Submandibular fossa (left) - 3. Left mandibular canal OR Left inferior dental/alveolar canal - 4. Left mental foramen - 5. Incisive branches & anterior loop of the mandibular canal **UWA DMF Radiology**                                                                                              **Dr Dayea Oh**  **Exercises** - Identify the type of x-ray - Identify anatomical structures / landmarks **Example** **Q. Type of x-ray?** A: Periapical radiograph (PA) of 35, 34, 33 → In radiology, Tooth # is counted from 18-28 (right to left), 38-48 (left to right) **Q. Anatomical structures/landmarks?** A: - 1. Mylohyoid ridge / internal oblique ridge - 2. Submandibular fossa (left) - 3. Left mandibular canal OR Left inferior dental/alveolar canal - 4. Left mental foramen - 5. Incisive branches & anterior loop of the mandibular canal A composite figure consisting of two panels. Panel A is a schematic diagram of the left mandible and adjacent teeth (molars), with five numbered callouts pointing to specific anatomical structures: 1 points to the mylohyoid ridge, 2 indicates the submandibular fossa, 3 highlights the mandibular canal, 4 marks the mental foramen, and 5 shows the incisive branches of the canal. Panel B is a corresponding grayscale periapical radiograph displaying the same dental anatomy. **Student Name:** 1. inferior cortex of mandible 2. inferior alveolar canal 3. lamina dura (radiopaque thin white line) 4. periodontal membrane space (radiolucent thin black line) 5. coronal pulp space (pulp chamber) 6. interproximal contact point 7. dentin 8. enamel 9. interseptal alveolar bone (interradicular alveolar bone) 10. crestal plate (thin white radiopaque line) 11. root canal space (containing the dental pulp) 12. cementum (frequently not distinguishable from the subadjacent dentin unless hypercementosis is present) UWA DMF Radiology Dr Dayea Oh   1. inferior cortex of mandible 2. inferior alveolar canal 3. lamina dura (radiopaque thin white line) 4. periodontal membrane space (radiolucent thin black line) 5. coronal pulp space (pulp chamber) 6. interproximal contact point 7. dentin 8. enamel 9. interseptal alveolar bone (interradicular alveolar bone) 10. crestal plate (thin white radiopaque line) 11. root canal space (containing the dental pulp) 12. cementum (frequently not distinguishable from the subadjacent dentin unless hypercementosis is present) A labelled anatomical diagram of mandibular teeth showing internal structures and surrounding bone. Labels include: 1 (inferior cortex of mandible), 2 (inferior alveolar canal), 3 (lamina dura), 4 (periodontal membrane space), 5 (coronal pulp space), 6 (interproximal contact point), 7 (dentin), 8 (enamel), 9 (interseptal alveolar bone), 10 (crestal plate), 11 (root canal space), and 12 (cementum). Arrows indicate specific anatomical relationships. A dental radiograph (X-ray) of the lower jaw showing multiple mandibular molars with visible root canals, enamel, dentin, periodontal ligament spaces, and surrounding alveolar bone structure. Student Name: UWA DMF Radiology Dr Dayea Oh 1. soft tissue shadow of upper lip 2. cervical margin (line) of enamel 3. alveolar bone margin (dark band between 2 and 3 is the root) 4. median maxillary suture 5. soft tissue outline of nose 6. incisive foramen   1. soft tissue shadow of upper lip 2. cervical margin (line) of enamel 3. alveolar bone margin (dark band between 2 and 3 is the root) 4. median maxillary suture 5. soft tissue outline of nose 6. incisive foramen Schematic diagram of maxillary anterior teeth and surrounding anatomy. The diagram includes labeled structures: 1 (soft tissue shadow of upper lip), 2 (cervical margin/line of enamel), 3 (alveolar bone margin with root indicated by dark band between 2 and 3), 4 (median maxillary suture), 5 (soft tissue outline of nose), and 6 (incisive foramen). Radiographic image of maxillary anterior teeth showing the corresponding anatomical landmarks seen in diagram A. Content: Student Name: **UWA DMF Radiology** Dr Dayea Oh 1. orifice of nasolacrimal duct (at infundibulum of the inferior turbinate not seen) 2. lateral wall of nasal fossa 3. #23 4. #24 5. #25 6. #21 7. #22 8. #63 9. #64 10. #65   1. orifice of nasolacrimal duct (at infundibulum of the inferior turbinate not seen) 2. lateral wall of nasal fossa 3. #23 4. #24 5. #25 6. #21 7. #22 8. #63 9. #64 10. #65 Labelled diagram of dental anatomy. The image shows a schematic representation of teeth and surrounding structures with numbered callouts. Key regions include: 1) orifice of nasolacrimal duct (at infundibulum of the inferior turbinate not seen), 2) lateral wall of nasal fossa, 3) tooth #23, 4) tooth #24, 5) tooth #25, 6) tooth #21, 7) tooth #22, 8) tooth #63, 9) tooth #64, and 10) tooth #65. Radiograph showing a close-up view of teeth and surrounding bone structure. The radiograph provides detailed imaging of the dental anatomy, complementing the labelled diagram on the left. **Student Name:** **1. embossed dot on film** **2. soft tissue outline of nasolabial fold** **3. floor of maxillary sinus** **4. bony septum in maxillary sinus** **5. air space of maxillary sinus** **6. metal part in bite-block** UWA DMF Radiology Dr Dayea Oh   1. embossed dot on film 2. soft tissue outline of nasolabial fold 3. floor of maxillary sinus 4. bony septum in maxillary sinus 5. air space of maxillary sinus 6. metal part in bite-block Annotated diagram of dental anatomy showing the maxillary sinus region. Labels include: 1 (embossed dot on film), 2 (soft tissue outline of nasolabial fold), 3 (floor of maxillary sinus), 4 (bony septum in maxillary sinus), 5 (air space of maxillary sinus), and 6 (metal part in bite-block). Clinical radiograph (periapical X-ray) of upper posterior teeth, displaying anatomical structures corresponding to the labeled regions in the adjacent diagram. Student Name: 1. zygomatic process of maxilla 2. hard palate/floor of nose 3. nasal mucosa 4. nasal cavity 5. maxillary sinus air space 6. sinus septum 7. floor of maxillary sinus 8. mucosa of alveolar ridge 9. alveolar bone of maxilla   1. zygomatic process of maxilla 2. hard palate/floor of nose 3. nasal mucosa 4. nasal cavity 5. maxillary sinus air space 6. sinus septum 7. floor of maxillary sinus 8. mucosa of alveolar ridge 9. alveolar bone of maxilla Labelled anatomical diagram of the maxillary region. The diagram features callouts with numbers pointing to specific structures: 1 is the zygomatic process of maxilla, 2 is the hard palate/floor of nose, 3 is nasal mucosa, 4 is nasal cavity, 5 is maxillary sinus air space, 6 is sinus septum, 7 is floor of maxillary sinus, 8 is mucosa of alveolar ridge, and 9 is alveolar bone of maxilla. Clinical radiograph (X-ray) showing a section of the maxilla with teeth. The image displays dental roots, alveolar bone, and the sinus floor area corresponding to the anatomy illustrated in Figure A. Student Name: UWA DMF Radiology Dr Dayea Oh 1. sinus floor mucosa 2. floor of maxillary sinus 3. zygomatic process of maxilla 4. air space of maxillary sinus 5. bony septum in maxillary sinus 6. sinus mucosa on both sides of septum 7. mucosal lining 8. soft tissue superimposition  1. sinus floor mucosa 2. floor of maxillary sinus 3. zygomatic process of maxilla 4. air space of maxillary sinus 5. bony septum in maxillary sinus 6. sinus mucosa on both sides of septum 7. mucosal lining 8. soft tissue superimposition Clinical figure showing two panels: Panel A is a labelled schematic diagram of the maxillary sinus region with numbered callouts (1–8) pointing to anatomical structures including the sinus floor mucosa, air space, and zygomatic process. Panel B is a corresponding dental radiograph displaying the same anatomy for diagnostic comparison. Student Name: UWA DMF Radiology Dr Dayea Oh 1. maxillary sinus air space 2. zygomatic arch 3. medial pterygoid plate 4. lateral pterygoid plate 5. hamular process of medial pterygoid plate 6. maxillary tuberosity 7. floor of maxillary sinus 8. coronoid process of mandible 9. embossed dot in film 10. “ks” marking indicating “D” speed film 11. bite-block  1. maxillary sinus air space 2. zygomatic arch 3. medial pterygoid plate 4. lateral pterygoid plate 5. hamular process of medial pterygoid plate 6. maxillary tuberosity 7. floor of maxillary sinus 8. coronoid process of mandible 9. embossed dot in film 10. “ks” marking indicating “D” speed film 11. bite-block Composite radiographic figure containing two panels: Panel A is a labeled diagram of a dental occlusal radiograph showing anatomical structures including the maxillary sinus air space (1), zygomatic arch (2), medial pterygoid plate (3), lateral pterygoid plate (4), hamular process of medial pterygoid plate (5), maxillary tuberosity (6), floor of maxillary sinus (7), coronoid process of mandible (8), embossed dot in film (9), ks marking indicating D speed film (10), and bite-block (11). Panel B is a corresponding clinical radiograph showing the same anatomy with visible teeth, roots, and surrounding bone structures. **Student Name:** 1. mental foramen (does not usually have a corticated margin) 2. inferior cortex of mandible UWA DMF Radiology Dr Dayea Oh   1. mental foramen (does not usually have a corticated margin) 2. inferior cortex of mandible Labelled diagram: Shows a schematic cross-section of mandibular teeth and surrounding bone. Label '1' points to a darkened area between the tooth roots, identified by OCR context as the mental foramen (noting it does not usually have a corticated margin). Label '2' points to the lower boundary of the bone structure, identified as the inferior cortex of mandible. Clinical radiograph: Displays an X-ray image of mandibular anterior teeth and supporting bone. The image corresponds to the diagram on the left, showing the natural appearance of the mental foramen region and the inferior cortex of the mandible without the stylized labeling present in the diagram. <div style="text-align: left;">1. inferior cortex 2. inferior cortical border 3. genial tubercles 4. lingual foramen 5. lingual canal 6. mental ridge 7. soft tissue shadow of lower lip</div>   1. inferior cortex 2. inferior cortical border 3. genial tubercles 4. lingual foramen 5. lingual canal 6. mental ridge 7. soft tissue shadow of lower lip Medical radiology figure containing two panels labeled 'A' and 'B'. Panel A is a labelled schematic diagram of the mandible showing anatomical structures with numbered callouts: 1 (inferior cortex), 2 (inferior cortical border), 3 (genial tubercles), 4 (lingual foramen), 5 (lingual canal), 6 (mental ridge), and 7 (soft tissue shadow of lower lip). Panel B is a corresponding clinical radiograph (X-ray) displaying the same anatomical region. Keyed list table providing definitions for the numbers used in Figure A. The entries are: 1. inferior cortex, 2. inferior cortical border, 3. genial tubercles, 4. lingual foramen, 5. lingual canal, 6. mental ridge, 7. soft tissue shadow of lower lip. Student Name: 1. genial tubercles 2. lingual foramen 3. inferior cortex 4. #31 5. #32 6. #73 7. #74 8. #33 9. #34 10. #35 UWA DMF Radiology Dr Dayea Oh    1. genial tubercles 2. lingual foramen 3. inferior cortex 4. #31 5. #32 6. #73 7. #74 8. #33 9. #34 10. #35 Labeled dental radiograph (Panel A) showing an occlusal view of the mandibular anterior region. It includes numbered callouts: 1 points to genial tubercles; 2 indicates lingual foramen; 3 shows inferior cortex; and tooth labels include #31, #32, #73, #74, #33, #34, and #35. Clinical periapical radiograph (Panel B) of the mandibular anterior teeth, corresponding to the anatomical landmarks shown in Panel A. Legend table mapping numbers from Panels A and B to anatomical structures and tooth identifiers: 1. genial tubercles, 2. lingual foramen, 3. inferior cortex, 4–10 correspond to specific tooth positions (#31 through #35). [^1]: Original PDF page 1: [[Lecture 4 Excercise answers.pdf#page=1|Lecture 4 Excercise answers, p.1]] [^2]: Original PDF page 2: [[Lecture 4 Excercise answers.pdf#page=2|Lecture 4 Excercise answers, p.2]] [^3]: Original PDF page 3: [[Lecture 4 Excercise answers.pdf#page=3|Lecture 4 Excercise answers, p.3]] [^4]: Original PDF page 4: [[Lecture 4 Excercise answers.pdf#page=4|Lecture 4 Excercise answers, p.4]] [^5]: Original PDF page 5: [[Lecture 4 Excercise answers.pdf#page=5|Lecture 4 Excercise answers, p.5]] [^6]: Original PDF page 6: [[Lecture 4 Excercise answers.pdf#page=6|Lecture 4 Excercise answers, p.6]] [^7]: Original PDF page 7: [[Lecture 4 Excercise answers.pdf#page=7|Lecture 4 Excercise answers, p.7]] [^8]: Original PDF page 8: [[Lecture 4 Excercise answers.pdf#page=8|Lecture 4 Excercise answers, p.8]] [^9]: Original PDF page 9: [[Lecture 4 Excercise answers.pdf#page=9|Lecture 4 Excercise answers, p.9]] [^10]: Original PDF page 10: [[Lecture 4 Excercise answers.pdf#page=10|Lecture 4 Excercise answers, p.10]] [^11]: Original PDF page 11: [[Lecture 4 Excercise answers.pdf#page=11|Lecture 4 Excercise answers, p.11]] [^12]: Original PDF page 12: [[Lecture 4 Excercise answers.pdf#page=12|Lecture 4 Excercise answers, p.12]] [^13]: Original PDF page 13: [[Lecture 4 Excercise answers.pdf#page=13|Lecture 4 Excercise answers, p.13]] [^14]: Original PDF page 14: [[Lecture 4 Excercise answers.pdf#page=14|Lecture 4 Excercise answers, p.14]] [^15]: Original PDF page 15: [[Lecture 4 Excercise answers.pdf#page=15|Lecture 4 Excercise answers, p.15]] [^16]: Original PDF page 16: [[Lecture 4 Excercise answers.pdf#page=16|Lecture 4 Excercise answers, p.16]] [^17]: Original PDF page 17: [[Lecture 4 Excercise answers.pdf#page=17|Lecture 4 Excercise answers, p.17]]